Use the formula p=le^kt. A bacterial culture has an initial population of 500. If its population grows to 7000 in 2 hours, what will it be at the end of 4 hours

Answers

Answer 1

Answer:

98,000 bacteria.

Step-by-step explanation:

We are given the formula:

[tex]P=le^{kt}[/tex]

Where l is the initial population, k is the rate of growth, and t is the time ( in hours).

We know that it has an initial population of 500. So, l is 500.

We also know that the population grows to 7000 after 2 hours.

And we want to find the population after 4 hours.

First, since we know that the population grows to 7000 after 2 hours, let's substitute 2 for t and 7000 for P. Let's also substitute 500 for l. This yields:

[tex]7000=500e^{2k}[/tex]

Divide both sides by 500:

[tex]e^{2k}=14[/tex]

We can solve for the rate k here, but this is not necessary. In fact, when can find our solution with just this.

Let's go back to our original equation. We want to find the population after 4 hours. So, substitute 4 for t:

[tex]P=500e^{4k}[/tex]

We want to find the total population, P. Notice that we can rewrite our exponent as:

[tex]P=500(e^{2k})^2[/tex]

This is the exact same thing we acquired earlier. So, we know that the expression within the parentheses is 14. Substitute:

[tex]P=500(14)^2[/tex]

Square and multiply:

[tex]P=500(196)=98000[/tex]

So, after 4 hours, there will be 98,000 bacteria.

And we're done!


Related Questions

Twelve decreased by twice a number equals -34. What is that number?

Answers

Answer:

12 - 2x = -34

Step-by-step explanation:

Im not entirely sure if this is correct but yeee

High Hopes^^

Barry-

Number is 23 because 12-2x=-34 is equivalent to the number 24

Mariah owed her grandfather $2.25 but was recently able to pay him back $1.50 how much does Mariah currently owe her grandfather

Answers

Answer:

$0.75

Step-by-step explanation:

2.25-1.50=0.75

If the variance of the data values in a population is 225, what is the standard
deviation of the data values?
a.15
b.17
c.11
d.13
(apex)

Answers

Answer:15

Step-by-step explanation:

Apex

How many hours will it take them to be 400 miles apart?

Answers

Step-by-step explanation:

50 miles per hour, how long will it take before that train meets THE Other train, going from B to A, at a speed

Jose and Fernando are both working at the same company. Jose worked 42 hours last week while Fernando worked 38 hours during the same week. Jose makes $15/hour and Fernando makes $16/hour. Who made more money that week?

Answers

Answer:

Jose

Step-by-step explanation:

Jose:

Step 1:

42 × 15        Equation

Step 2:

$630     Multiply

Fernando:

Step 1:

38 × 16      Equation

Step 2:

$608    Multiply

Answer:

Jose earns more

Hope This Helps :)

Which ratio is equivalent to 3:7?
A 6:7
B 3:21
C 24:56
D 15:30

Answers

Answer:

c

Step-by-step explanation:

Answer:

C. 24:56

Step-by-step explanation:

3/7 * 8/8

3*8 = 24

7*8 = 56

24/56

Express in the form n : 1
30 : 6

Answers

30/6 = n
n = 5
ratio is 5:1

Answer:

5:1

Step-by-step explanation:

Jasmine paid $64.50 for a bracelet, after tax, and the tax rate is 7.5%. What was the original price of the bracelet?

Answers

Answer:

About $59.66

Step-by-step explanation:

To find the amount of tax was paid, multiply 64.50 by 0.075 (because 0.075 = 7.5%). This would be 4.8375, which when rounded is 4.84. You subtract 64.50 by 4.84 to get 59.66, but because I rounded, it is about $59.66.

Answer:

60

Step-by-step explanation:

First, change the percentage to a decimal and write the equivalence of the sales tax amount. Let x be the original cost of the item.

Sales tax amount =x⋅0.075

Next, substitute the value into the equation:

Original Cost + Sales Tax Amount = Total Cost

x+0.075x=64.50

Add like terms.

1.075x=64.50

Divide both sides by 1.075 to isolate the unknown value.

x=$60

A coordinate plane with 4 lines. The first line is labeled a(x) and passes through (2, negative 4) and (0, 2) and continues past (negative 1, 5). The second line is labeled f(x) and passes through (negative 6, negative 6), (negative 3, 0), and (0, 6). The third line is labeled g(x) and passes through (negative 2, negative 7), (0, negative 3), (1, negative 1) and (2, 1). The fourth line is labeled h(x) and passes through (negative 6, negative 6), (0, negative 3), and (6, 0).
When Janelle woke up, it was –3 degrees Fahrenheit outside. As the morning progressed, the temperature rose 2 degrees every hour.

Which line on the graph could represent this scenario?

a(x)
f(x)
g(x)
h(x)

Answers

Answer:

It is c which is g(x)

Step-by-step explanation:

Answer:

the answer is C : g(x)

Step-by-step explanation:

i just got the right answer on the assignment

Could someone help me with number 17.

Answers

Answer:

y=-7

Step-by-step explanation:

if g(x)  is g(-2) that means that x=-2 so we plug that in so 5*-2+3

5*-2+ -10  

-10+3+ -7

so y=-7

The Answer to the question is: Y= -7

Which graph represents the inequality y < -1 + 2x?

Answers

Answer:

The graph is attached down

Step-by-step explanation:

The form of the linear inequality is y < b + m x, where

m is the slope of the lineb is the y-intercept, the point of intersection between the line and the y-axis (0, b)The solution of the inequality is the area under the line  

To find which graph represents the inequality y < -1 + 2x

→ Find the y-intercept (the value of y at x = 0)

∴ b = -1

∴ The y-intercept is (0, -1)

From the given graphs we have two graphs that the line intersected the y-axis at (0, -1)

2nd graph in the 1st row

2nd graph in the 2nd row

∵ The sign of inequality is <

∴ The shaded area must be under the line

∴ The 2nd graph in the 1st row is our answer

The graph which represents the inequality y < -1 + 2x is attached down

1 point
3. A bus driver stops at a gas station to put some gasoline in the bus. He
pays $2.48 per gallon for 15 gallons of gas. How much did he pay for the
gas?

Answers

hmmm i think it’s $37.20

A local hamburger shop sold a combined total of 700 hamburgers and cheeseburgers on Tuesday . There were 50 more cheeseburgers sold than hamburgers . How many hamburgers were sold on Tuesday

Answers

Answer:

325

Step-by-step explanation:

h + c = 700

c = 50 + h

50+ h + h= 700

50+2h =700

2h=700-50

2h = 650

h=650/2

h=325

c=325+50

c=375

check 325+375=700

Cindy and Victoria completed 8/9 of their job in a day. Cindy has done 1/9 of the work. How much of the work was done by Victoria?

Answers

Answer:

7/9 of the work was done by Victoria.

Step-by-step explanation:

8/9-1/9=7/9

Solve the equation

6=u/9+10

Answers

Answer:

114

Step-by-step explanation:

Because u do 9+10 which equals 19 and then u do 19*6 and u get 114 so the expression now would be 6=114/(9+10)

The graph shows f (x) and its transformation g(x) . Which equation correctly models g(x) ?
A) g(x) = 4x-2 + 4
B) g(x) = 4x+2 - 4
C) g(x) = 4x+4 + 2
D) g(x) = 4x-4 + 2

Answers

C because of the climax an it rises vertically to the y axis

Karen can walk 2/3 of a mile in 1/5 of an hour. How long will it take her to walk 10 miles

Answers

Answer:

3 1/3 mph

Step-by-step explanation

2/3 mile divided by 1/5 hour

To divide by a fraction, MULTIPLY BY THE RECIPROCAL!

This gives 5(2/3) = 10/3 = three & 1/3 mile per hour, or about 3.33 mph.

what percent of 50 is 18?

Answers

Answer:

36 %

Step-by-step explanation:

Convert the fraction to a decimal, then multiply by  100 .

Answer:

36%

Step-by-step explanation:

The same explanation as she said

In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .75, the same as the overall proportion of complaints settled in 2008
a. Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of .
b. Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
c. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of .
d. Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?

Answers

Answer:

a) the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204

b) the probability that the sample proportion will be within 0.04 of the population proportion is 0.95

c) sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061

d) the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088

e) gain in precision is 0.1402.

Step-by-step explanation:

a) Let p represent the

Given that

population proportion of complaints settled for new car dealers p = 0.75.

and n = 450

mean of the sampling distribution of the sample proportion is the population proportion p

i.e  up° = p

mean of the sampling distribution of the sample proportion p° = 0.75

so standard error of the proportion is;

αp° = √(p( 1-p ) / n)

we substitute

αp° = √(0.75 ( 1-0.75 ) / 450)

=√(0.1875 / 450

= √0.0004166

= 0.0204

therefore the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204

b)

(p° - p) is within 0.04

so lets consider

p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 450)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 450))

= p( -0.04/0.0204 ≤ z ≤ 0.04/0.0204)

= p ( -1/96 ≤ z ≤ 1.96 )

= p( z < 1.96 ) - p( z < -1.96 )

now from the S-normal table,

area of the right of z = 1.96 = 0.9750

area of the left of z = - 1.96 = 0.0250

p( -0.04 ≤ p°- p ≤ 0.04)  =  p( z < 1.96 ) - p( z < -1.96 ) = 0.9750 - 0.0250

= 0.95

therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.95

c)

population proportion of complaints settled for new car dealers p = 0.75.

n = 200

mean of the sampling distribution of the sample proportion p°.

i.e up° = p

mean of the sampling distribution of the sample proportion p° = 0.75

Sampling distribution of the sample proportion p is determined as follows

αp° = √(p( 1-p ) / n)

we substitute

αp° = √(0.75 ( 1-0.75 ) / 200)

=√(0.1875 / 200

= √0.0009375

= 0.03061

therefore sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061

d)

(p° - p) is within 0.04

so lets consider

p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 200)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 200))

= p( -0.04/0.03061≤ z ≤ 0.04/0.03061)

= p ( -1.31 ≤ z ≤ 1.31 )

= p( z < 1.31 ) - p( z < -1.31 )

now from the S-normal table,

area of the right of z = 1.31 = 0.9049

area of the left of z = - 1.31 = 0.0951

p( -0.04 ≤ p°- p ≤ 0.04)  =  p( z < 1.31 ) - p( z < -1.31 ) = 0.9049 - 0.0951

= 0.8098

therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088

e)  

From b), the sample proportion is within 0.04 of the population proportion; with the sample of 450 complaints involving new car dealers is 0.95.

sample proportion is within 0.04 of the population proportion; with the sample of 200 complaints involving new car dealers is 0.8098.

measured by the increase in probability, gain in precision occurs by taking the larger sample in part (b)

i.e

Gain in precision will be;

0.9500 − 0.8098

= 0.1402

therefore  gain in precision is 0.1402.

What is the quotient for 6 and 1/2 divided by 3/4

Answers

Answer:

I believe it is 4

Step-by-step explanation:

Which expression is equivalent to Sine (StartFraction pi Over 12 EndFraction) cosine (StartFraction 7 pi Over 12 EndFraction) minus cosine (StartFraction pi Over 12 EndFraction) sine (StartFraction 7 pi Over 12 EndFraction)?

Answers

Answer:

EndRoot Over 2 EndFraction

StartFraction pi Over 6 EndFraction, StartFraction StartRoot 3 EndRoot Over 2 EndFraction

On using the trigonometric identity sin(x-y) = sin(x)cos(y) - cos(x)sin(y), we calculate that  [tex]sin(\frac{\pi }{12})cos(\frac{7\pi }{12}) - cos(\frac{\pi }{12} )sin(\frac{7\pi }{12} ) =sin(\frac{-\pi }{2} )[/tex].

What are trigonometric identities?

Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain.

[tex]=sin(\frac{\pi }{12})cos(\frac{7\pi }{12}) - cos(\frac{\pi }{12} )sin(\frac{7\pi }{12} ) \\\\=sin(\frac{\pi }{12} -\frac{7\pi }{12})\\ \\ =sin(\frac{-\pi }{2} )[/tex]

Learn more about trigonometric identities here

https://brainly.com/question/12537661

#SPJ3

Givin (2, 4) and 6, 12), what is The slope of the line between these two points?

Answers

Answer:

m=4 or slope =4

Step-by-step explanation:[tex]m=\frac{y2-y1}{x2-x1\\}[/tex]

so [tex]m=\frac{12-4}{6-2}[/tex] which is the same as 8/2. So all in all the slope is 4.

Perform he operations in the correct order :
10 + 8 ÷ 1 -5

Answers

The answer is 13 !!!
if you want work:

step 1: divide first (8 divided by 1 = 8)
step 2: add since it’s first (10 + 8 = 18)
step 3: subtract (18 - 5 = 13)

hi guys please help me to solve the following question

Answers

Answer:

D!

Step-by-step explanation:

To find the area, we multiply the length times the width to find the number of squares in each box.

A) 1 square down times 7 squares across is 1 x 7, which is 7.

B) 2 squares down times 6 squares across is 2 x 6= 12.

C) 3 squares down times 5 squares across is 3 x 5 = 15.

D) 4 squares down times 4 squares across = 4 x 4 =16.

16 is the biggest number here, so that is the greatest area!

If you enjoyed my answer, please give it a rating and a Thanks! If you think this answer was pretty brainly, please give it a Brainliest!

Have a great day!

What is 3/5 written as a percent? A. 6% B. 30% C. 60% D. 167%

Answers

Answer:

60%

Step-by-step explanation:

It is 60% because, First we have to make 3/5 a percent so we do 5 times 20 which is 100, and 3 times 20 which is 60. So it total it is 60/100 which is 60%

Answer:

[See Below]

Step-by-step explanation:

_________________________________

An easier way of doing this is to change the fraction to an equivalent fraction:

[tex]\frac{3}{5}[/tex] ≅ [tex]\frac{6}{10}[/tex] ≅ [tex]\frac{60}{100}[/tex]

So now it's easier to change to a percentage.

[tex]\frac{60}{100} =60\%[/tex][tex]60[/tex] percent of [tex]100[/tex]

_________________________________

So your answer would be:

[tex]\bold6\bold0\bold\%[/tex]

_________________________________

~Hope this helps Mate. If you need anything feel free to message me.

[tex]-Your~ Friendly~ Answerer,~ Shane[/tex]

Find the median of the following data
2,8,7,8,6,15,6,8,3

Answers

Answer:

7

Step-by-step explanation:

Median is the middle value in a list of values arranged in increasing order.

The values given are :2,8,7,8,6,15,6,8,3

Arrange values in ascending order as: 2,3,6,6,7,8,8,8,15

The middle value is: 2,3,6,6,7,8,8,8,15

Median is 7

Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
Ps. I just need h(x)

Answers

The answer is C hoped this helped

NEED HELP GIVING 15 POINTS

Choose the one problem that has NOT been done correctly. Start your response with the number you choose and explain the mistake that was made in the problem.

Answers

Answer:

1

Step-by-step explanation:

didn't mulitiply by -2

2
it says y=-4 (2 x -4)=-8
7-(-8) turns into 7+8 because two negatives make a positive

Help ASAP
Find the sum (-3x + 7) + (2x - 5).

Answers

Answer:

-x + 2

Step-by-step explanation:

Given (64y^2)+(4x^2)+128y+16x+64=0, transform the equation into the appropriate form

Answers

Answer:

(8y+8)²+(4x²+16)=0

Step-by-step explanation:

Given:

(64y²)+(4x²)+128y+16x+64=0

Find:

Equation into the appropriate form

Computation:

(64y²)+(4x²)+128y+16x+64=0

(8y)²+(2x)²+128y+16x+64=0

(8y)²+(2x)²+2(8y)(8)+2(2x)(4) + 8²=0

(8y+8)²+(4x²+16)=0

Other Questions
6.) The length of a rectangle is 19 feet longer than the width. If the perimeter is 46feet, write an equation for this scenario where "x" represents the width. You buy 3.18 pounds of pears, 1.45 pounds of oranges , and 2.79 pounds of peaches what is your total billpears-0.99 per poundoranges-1.19 per pound peaches-1.29 per pound (round to the nearest cent) Why did slavery come to a halt in the 1750s? all living things must have their basic needs met to survive and can only live in habitats that meet their needs. living things need food,air,sunlight,and Arrange the steps for measuring heart rate in the correct order from start to finish.a. Make a fist.b. Feel a pulse.c. Count for 10 seconds.d. Find a radial artery.e. Multiply by six.A. a, d, b, e, cB. d, a, b, e, cC. a, d, b, c, eD. d, a, b, c, e Is the conflict between Israel and Palestine caused by land, religion, or both? Write a short response to explain your thinking. Provide examples and evidence from the text to support your response. How do I round up this number 86,088 Explain how wars and conquests affect social change. what are intensive pronouns? 3 2= 2 84 I dont know how to do this A proton travels through uniform magnetic and electric fields. The magnetic field is in the negative x direction and has a magnitude of 3.54 mT. At one instant the velocity of the proton is in the positive y direction and has a magnitude of 2230 m/s. At that instant, what is the magnitude of the net force acting on the proton if the electric field is (a) in the positive z direction and has a magnitude of 5.25 V/m, (b) in the negative z direction and has a magnitude of 5.25 V/m, and (c) in the positive x direction and has a magnitude of 5.25 V/m How are mitosis and meiosis similar?A. They both produce tetrads.B. They both involve duplicating chromosomes C. They both produce gametesD. They both increase the chromosomes number. How do we indentify news flash in the television Ratio of dolls to teddy bears is 6:5. There are 240 dolls, how many teddy bears? Newton has 10 more dimes than nickels. He hastwice the number of quarters than nickels. If hehas $6.20, how many of each coin does he have? Solve the system x+2z=30 y+z=12 z=1 Which of the following describes Inskeeps opinion on Rwandas democracy?Rwandas recovery since the genocide has been impressive, but Kagames term length is concerning.Rwanda is not really a democracy, but that is a minor concern given all of the problems the country has had in the past.Rwandas democracy is complete and fully flourishing in the face of extraordinary challenges.The road ahead will be full of challenges, but Kagame is the right person to continue leading the country. The chemicals in the brain that send messages from one nerve ending toanother are called: Help ASAP)Instructions: Complete the sentences by typing in the words that are missing. Some letters are provided. ( Took a picture). Please Only Answer If Your Good With Spanish. Will Mark Brainliest Are corals minerals? Why?