An astronaut was exploring the moon of a distant planet, and found some glowing goo at the bottom of a very deep crater. She brought a 10-gram sample of the goo to her laboratory. She found that when the goo was exposed to light, the total amount of goo increased by 100% every hour.
How much goo will she have after 1 hour? After 2 hours? After 3 hours? After n hours?
When she put the goo in the dark, it shrank by 75% every hour. How many hours will it take for the goo that was exposed to light for n hours to return to the original size?

Answers

Answer 1

The amounts of goo after each hour are given as follows:

1 hour: 20 grams.2 hours: 40 grams.3 hours: 80 grams.n hours: 10(2)^n.

The time that it takes for the goo to return to original size is given as follows:

n hours, for which:

[tex](2)^n(0.25)^n = 1[/tex]

How to model the situation?

An increasing exponential function is defined as follows:

y = a(1 + r)^x.

For which the parameters are given as follows:

a is the initial value.r is the growth rate, as a decimal.

Her sample is of 10 grams, and the amopunt of goo increases by 100%, hence the parameter values' are given as follows:

a = 10, r = 1.

Thus the exponential function is defined as follows:

y = 10(2)^n.

Then the amounts are given as follows:

One hour: y = 10 x 2 = 20 grams.Two hours: y = 10 x 2² = 40 grams.Three hours: y = 10 x 2³ = 80 grams.

A decreasing exponential function is given as follows:

y = a(1 - r)^x.

The goo shrinks by 75% every hour, hence:

r = 0.75.

The amount after n hours is of 10(2)^n, hence the shrinking function is given as follows:

[tex]y = 10(2)^n(0.25)^n[/tex]

It returns to the original amount when:

y = 10.

Hence:

[tex]10 = 10(2)^n(0.25)^n[/tex]

[tex](2)^n(0.25)^n = 1[/tex]

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Related Questions

the point (2, 6) is located on a line with slope of 3. which point could also be located on the line?​

Answers

Answer

using y = mx+c

where m is the slope and c

6 = 3(2)+c

6 = 6 + c

c= 0

Y-intercept is where the line passes through the y-axis, which is where x = 0

So, when x = 0, y = 0

Another point on the line, then, is {0,0}

Claire tosses a coin and rolls a number cube 100 times. How many times should she expect to have the coin show heads and roll a 1 or 2?

Answers

F. 17 would be your answer I believe







Please someone help me !!

Answers

Answer: $26.81

Step-by-step explanation: the tank holds 16.5 gallons. Meaning, half of the tank is 8.25 gallons. Multiply that by the cost of the gas, 3.25, and you get 26.81

Add 1.8m, 77cm, 210mm and give your answer in cm

Answers

The total length is 2.077m (2177 cm).

What is length?

Length is a measurement of size, distance, or duration. It can refer to physical size (length of a field, length of an object, etc.), distance (length of a journey, length of a river, etc.), or duration (length of a movie, length of a school day, etc.). Length can also refer to the duration of time it takes to complete something (length of a task, length of a process, etc.). Length is typically measured in units such as meters, feet, inches, miles, kilometers, and seconds.

The given measurements can be added together to calculate a total length. The addition of 1.8m, 77cm, and 210mm can be expressed in the form of a sum equation. The equation would be 1.8m + 77cm + 210mm = ?.

To solve this equation, the measurements need to be converted to the same unit of measurement. In this case, all measurements can be converted to cm. 1.8m is equal to 1800cm, 77cm is equal to 77cm, and 210mm is equal to 21cm.

Therefore, the sum equation becomes 1800cm + 77cm + 21cm = ?. To find the total length, the numbers can be added together.

The total length is 1977cm. However, since the measurements are expressed in decimals, the answer must also be expressed in decimals. Therefore, the total length is 2.077m (2177 cm).

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An aquarium holds 11.5 cubic feet of water, and is 2.2 feet long and 1.6 feet wide. What is its depth??

The depth is _____ feet.​

Answers

Answer: 3.52

Step-by-step explanation:

Hey!

So for this problem, we need to follow the Volume formula which is:

length x width x height

We know our length and width so all we need is our height (depth)

First , We multiply our length and width.

2.2 x 1.6 = 3.52

Next, we figure out what times this will equal 11.5. We can see that this number can’t be times 4 because that would make it twelve so we need to lower it. We can divide 11.5 (the volume) by 3.52 to get our answer.

We get 3.267. Rounded to the hundredths it would be 3.27 ft.

Hope this helps! :D

Sorry if I messed anything up!

Comment down below if you have any further questions!

The florist sells roses, carnations, tulips, daisies, and violets. How many ways can he choose three types of flowers for an arrangement?

Answers

What are the options

PLEASE HELP! I WILL GIVE BRAINLIEST! Doug bought a meal in a town that has no sales tax. He tips 20%. Select all meals that Doug could buy for $20 or less. SELECT ALL CORRECT ANSWERS
A.$17.15
B.$16.50
C.$16.80
D.$16.65
E.$15.25
F.$17.00

Answers

Answer: E and B are the right answer I think tell me if im wrong :)

PLS PLS HELP I HAVE A D IN MATH AND NEED HELP GETTING MY GRADE UP

Answers

Answer:

1/6 bcause

Step-by-step explanation:

it is a 4 by 3 block so if your going to count cont by the side answe is 1/6

if a sample proportion is 0.85, which range of possible values best describes an estimate for the population parameter?
A. (0.8, 0.85)
B. (0.8, 0.89)
C. (0.85, 0.9)
D. (0.8, 0.9)

Answers

Answer:

The correct answer is (0.8, 0.9)

(0.8+0.9) divide by 2 = 85

:) hope this helps

Step-by-step explanation:

Which graph represents an exponential function?

Answers

Answer:

The answer to your question is the third one

Step-by-step explanation:

The first graph is the graph of a

The second graph is of a rational function

The third one is of an exponential function

(2m + 1) * x ^ 2 - (2m + 5) * x + (2m + 1) = 0

Answers

Answer:

(2m + 1) * x ^ 2 - (2m + 5) * x + (2m + 1) = 0

2mx^2+x^2-2mx+5x+2m+1=0

3mx^2+5x+1=0

That's as far as you can get simplifying it.

Step-by-step explanation:

express the following ratios as fractions in their lowest term
a.4 birr to 16 cents
b.5 days to 100 hrs​

Answers

Answer:

1/4 is A and 1/20 is B

Step-by-step explanation:

Not much of an explanation needed

The ratios 4 birr to 16 cents and 5 days to 100 hrs can be expressed as [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{20}[/tex] in their lowest terms.

What is Ratio?

Ratio is the relationship between two quantities which shows the number of times that the one quantity is contained within the other quantity.

If 'a' is related to 'b', they can be denoted in terms of ratio as a : b.

Ratios can be expressed as fractions.

(a) 4 birr to 16 cents = [tex]\frac{4}{16}[/tex]

The highest common factor of both 4 and 16 is 4.

[tex]\frac{4}{16}[/tex] = (4 × 1) / (4 × 4) = [tex]\frac{1}{4}[/tex]

(b) 5 days to 100 hrs = [tex]\frac{5}{100}[/tex]

The highest common factor of 5 and 100 is 5.

[tex]\frac{5}{100}[/tex] = (5 × 1) / (5 × 20) = [tex]\frac{1}{20}[/tex]

Hence the ratios can be expressed as [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{20}[/tex] in their lowest terms.

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The cost of an amusement park ticket has been increasing by the same percentage since 2000.
a. The equation c(t)=80(1.03)^t represents the cost of a ticket in dollars as a function of tea the number of years since 2000 explain what the 80 and 1.03 tells us about the situation
b. what is the percent increase in to get prize from year to year?
what does c(5) mean in the situation? find its value and show your reasoning

Answers

a. 80 tells you the ticket price in the year 2000, 1.03 tells you that the ticket price increases by 3% every year

b. c(5) means what the cost of the ticket in 2005 is, it’s value is 92.74 because 80(1.03)^5 is 92.74

Find one value of x that is a solution to the equation:
(3x + 7)2 = -6x – 14

Answers

Answer: x = -7/3

Step-by-step explanation:

https://www.symbolab.com/solver/step-by-step/%5Cleft(3x%20%2B%207%5Cright)2%20%3D%20-6x%20-%2014

there are the steps

Answer:x=-7/3

                   

Step-by-step explanation:(3x+7)(2)=−6x−14

(3x)(2)+(7)(2)=−6x+−14(Distribute)

6x+14=−6x+−14

6x+14=−6x−14

6x+14+6x=−6x−14+6x

12x+14=−14

12x+14−14=−14−14

Find the value of the trigonometric ratio.

Answers

Answer:

A) 12 / 13

Step-by-step explanation:

The Sine of a number is defined as the ratio of the length of the side opposite the angle, divided by the length of the hypotensue.

As a member of the United Nations, you must consider each of the following proposals. In each case, assume that the United Nations would like to receive as many emergency supplies as possible, while still having each nation give equally.
a. One proposal is that each country gives medicine packages. How many food packages should the United Nations require from each country in this case? Explain how you made your decision.
b. Another proposal is to get the largest number of medicine packages possible. What is the largest number of medicine packages that each country can offer? How did you find your answer?

Answers

Answer:

Following are the solution to the given question:

Step-by-step explanation:

For point a:

Initially, we have had to figure out how many packaged food the country should offer with both the biggest quality and then the number of packages each country should give.

Find out just how many food packages a nation should donate with both the lowest budget.

For point b:

They first need to figure out just how many medication packages the country should donate on the lowest budget, and then how many packages each country can donate.

Find out just how many medicinal packets the smallest budget nation can donate.

darius and dakota re roommates. together they have 238 books. if darius has 50 more books than dakota, how many books does dakota have? write an algebraic equation using x for a variable for the situation and solve for x​

Answers

Answer:

Dakota has 94 books, while Darius has 144.

Step-by-step explanation:

Given that Darius and Dakota are roommates, and together they have 238 books, if Darius has 50 more books than Dakota, to determine how many books does Dakota have the following calculation must be performed:

Dakota = X

Darius = X + 50

X + X + 50 = 238

2X + 50 = 238

2X = 238 - 50

X = 188/2

X = 94

Therefore, Dakota has 94 books, while Darius has 144.

The square root parent function is translated so that it has an endpoint located at (4,-1), then
vertically compressed by a factor of 1/3. Write an equation that could represent this function.
PLEASE HELP

Answers

Answer:

Step-by-step explanation:

[tex]parent~function~f(x)=\sqrt{x-4} -1\\new ~function ~g(x)=\frac{1}{3} \sqrt{x-4}-1[/tex]

Using translation concepts, an equation that could represent this function is:

[tex]f(x) = \frac{1}{3}(\sqrt{x - 4} - 1)[/tex]

The square root parent function is given by:

[tex]f(x) = \sqrt{x}[/tex]

The endpoint is (0,0).

What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

After the translation:

The endpoint is (4,-1), hence it was shifted 4 units right and 1 unit down, which means that the equation is now:

[tex]f(x) = \sqrt{x + 4} - 1[/tex]

Vertically compressed by a factor of [tex]\frac{1}{3}[/tex] means that it was multiplied by [tex]\frac{1}{3}[/tex], hence:

[tex]f(x) = \frac{1}{3}(\sqrt{x - 4} - 1)[/tex]

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A machine at a graphic design studio produces paper labels for juice bottles. This graph represents the number of labels produced over time.

Zoom in if you cannot see!

Don’t answer if you don’t know the answer. Whoever gets the correct answer will get Brainliest! :)

Answers

Answer:

Option B, would be the correct answer: 75 labels per minute

Step-by-step explanation:

The number of labels produced per minute would be a constant value which would be the slope of this graph represented above.

Slope = [tex]\frac{rise}{run}[/tex]

Slope = [tex]\frac{150}{2}[/tex]

Slope = 75

Hope this helps!

I think it’s 150 since 1 minute= 150 labels

The perimeter of a rectangular lawn is 108 meters it is 35 meters long how wide is it

Answers

Answer:

19 meters

Step-by-step explanation:

1. 35×2= 70

2. 108-70=38

3. 38÷2=19

I hope that helped☺

correct answers only, if you send me a link then you will be reported

Answers

Answer:

c

Step-by-step explanation:

BC is tangent to ⊙A at point B. What is the value of x?

Answers

The value of x is 6 or 3.5.

What is Pythagoras theorem?

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

We have,

Radius = (x-2)

CB= 2x -9

Using Pythagoras theorem

AB² + CB² = AC²

(x-2)² + (2x-9)² = (x-2+1)²

x² + 4  -4x + 4x² + 81 - 36x = x² + 1 -2x

4x² -38x + 84 = 0

Solving the quadratic equation we get

x= 6 or 3.5

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Devika is making porridge by following this recipe.
She has 4 pints of milk and plenty of other ingredients.
What is the maximum number of whole servings she can make?
Note: 1 pint = 568 mL
Recipe: Serves 1
40 g oats
300 mL milk

Answers

4 pints x 568ml = 2272ml (this is how much milk she has)

2272ml divided by 300ml (the amount the recipe asks for) = 7.573...

round it down to get the nearest whole number, you end up with 7. (you can’t round it up to 8, because she has less than the amount needed for 8 servings)

so, the maximum number of whole servings she can make is 7.

Multiply the fractions. Select the answer that is in simplest form.
1
1
5- X 1 = ?
2
4
OA.
1
5
8
OB
1
6
4
OC.
7
6-
8

Answers

Answer:

1 is factors of this question

Answer:

a.option is your answer

You're creating plans for a building project, and you use a T-square to create a set of angles from lines that are perpendicular, meaning the lines are at right angles to each other, or ______ degrees? a. 225, b. 45, c. 180, d. 90

Answers

Answer:

d. [tex]90^{\circ}[/tex]

Step-by-step explanation:

This is the definition of perpendicularity.

A pile of sand has a weight of 90 kg.
The sand is put into a small bag, a medium bag and a large bag
in the ratio 2:3:7.
Work out the weight of sand in each bag.
but

Answers

Answer:

i hope it helps

mapriend

Answer:

Step-by-step explanation:

divide 90 by 2, 3, 7

small bags 90 ÷ 2 = 45

medium bag 90 ÷ 3 = 30

large bag 90 ÷ 7 = 12.8 round it to nearet whole number = 13

Which measure would change if you replaced 67 with 115
23, 89, 15, 67, 32, 41
A. Lower quartile
B. Mean
C. Mode
D. Median
HELP PLEASE! ​

Answers

Mean
As this value is greater than 67 and the highest number in original sequence

Ben is walking 150 miles in 31 days to raise money for a charity. He wants to walk the same distance each day. How far should he walk each day?

Explain what you did with the remainder and why.

Answers

If he wants to walk the same distance everyday, you should divide the number of miles on the days.
150/31 = 4.8 miles per day

Calculate the lengths of the 2 unlabeled sides. Round answers to the nearest tenth, if necessary.

Answers

Answer:

JG = 6.5 & JH = [tex]6.5 *\sqrt{2}[/tex] or 9.192388155

Step-by-step explanation:

45-45-90 triangles follow a pattern in which the smallest sides are equal & we represent them by x.

The hypotenuse is equal to [tex]x*\sqrt{2}[/tex]

So that's how we find our answers :0)

A six sided die is rolled two times arrange the events in order from the event with the highest probability to the event with the lowest probability

Answers

Answer:

6

Step-by-step explanation:

A six sided die is rolled two times arrange the events in order from the event with the highest probability to the event with the lowest probability  

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