Free Printable Let's Begin Exponential Growth and Decay

1.

Type in your answer to: Based on your notes, if the base "b" in the exponential equation $y=a\cdot b^x$ is greater than one, the graph models exponential (a) .

2.

Looking at notes 12.1, go to the graph at the bottom of the page. Reading the x/y chart...when x = -2, y = (a)

3.

What are the domain and range of $y=e^x$ ?

a)

D: $\left(-\infty,\ \infty\right)$

b)

D: $\left(0,\ \infty\right)$

c)

R; $\left(0,\ \infty\right)$

d)

R: $\left(-2,\ \infty\right)$

4.

Describe the transformations to the parent graph: $y=e^{\left(x+3\right)}-4$

a)

left 3, down 4

b)

right 3, down 4

c)

left 4, up 3

d)

right 3, up 4

5.

$y=a\left(1+r\right)^t$ In this exponential growth model, what do a and r represent?

a)

"a" represents original amount

b)

"a" represents the ending amount

c)

"r" represents the growth rate written as a decimal

d)

"r" represents the radius of the equation

6.

For the compound interest formula, what do n and t represent?

a)

n represents the number of items in the equation

b)

n represents the number of compoundings of interest per year

c)

t represents time

d)

t represents the rate of growth

7.

When looking at the compound interest formula, if your bank compounds interest monthly, the "n" value would be 12. Now your bank decides to compound interest quarterly, what is the new value of n? n = (a)

8.

$A=Pe^{\left(rt\right)}$ is the formula you use if growth is compounded continuously. What does P represent?

a)

The ending population

b)

The initial population

c)

The percentage of grwoth

9.

Select all the equations that model exponential growth. Look closely at the number with the exponent.

a)

$y=3^x$

b)

$y=\frac{1}{2}\left(5\right)^x$

c)

$y=3\left(\frac{1}{2}\right)^x$

d)

$y=\left(\frac{1}{4}\right)^x$

10.

You deposit $500 in an account that earns 2.2% annual interest. Find the balance after 2 years if interest is compounded quarterly.

a)

$533.12

b)

$524.77

c)

$522.43

d)

$521.48

11.

You purchase a new computer for $1500 and it depreciates (goes down in value) by 20% per year. Which equation would you use to find its value after 3 years?

a)

$y=.2\left(1500\right)^3$

b)

$y=1500\left(1-.2\right)^3$

c)

$y=20\ \left(1500-1\right)\left(3\right)$

d)

$y=1500\left(1-20\right)^3$

12.

You started with 4 cells in a petri dish in your lab and the cells are growing at a rate of 12.3% (per minute) compounded continuously. Pick the equation that shows the amount of cells after just 10 minutes.

a)

$A=4e^{\left(\left(.123\right)\left(10\right)\right)}$

b)

$A=10e^4$

c)

$A=4e^{1230}$

d)

$A=4e^{\left(.123\right)}$

13.

Thinking back to our unit on exponents, simplify the following expression: $e^3\cdot e^5$

a)

$e^{15}$

b)

$e^8$

c)

$e^{-2}$

d)

$e^{3.5}$

14.

Based on your knowledge of exponents, simplify: $\left(3e^{-2}\right)^{-3}$ Recall this hint: $2^{-3\ }=\frac{1}{8}$

a)

$3e^{-6}$

b)

$-27e^{-6}$

c)

$\frac{e^6}{27}$

d)

$\frac{e^{-6}}{-27}$

15.

You have $1000 to invest at your bank which compounds the interest twice a year at an interest rate of 5%. How much money is in your account at the end of one year?

a)

$1005.78

b)

$1050.63

c)

$1000

d)

$1500.12

16.

You just finished enjoying a beverage that contains 120 mg of caffeine. Each hour the caffeine in your system it decreases by 12%. Assuming you have had no more caffeine, how many mg are still in your system (from your original beverage) after 8 hours?

a)

42.175 mg

b)

28.113 mg

c)

14.798 mg

d)

43.156 mg

Let's Begin Exponential Growth and Decay

Total questions: 16

Worksheet time: 8mins

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