Free Printable Exponential Functions and Geometric Sequences

1.

Is this exponential growth or decay?

a)

Growth, the common ratio is between 0 and 1.

b)

Decay, the common ratio is between 0 and 1.

c)

Growth, the common ratio is greater than 1.

d)

Decay, the common ratio is greater than 1.

2.

The relationship between time and population is ________________.

a)

Exponential growth

b)

Exponential decay

c)

Linear, and increasing

d)

Linear, and decreasing

3.

What type of function is

$f\left(x\right)=2\cdot\left(\frac{1}{7}\right)^x$

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Above

4.

Select the TRUE statements about the functions

$f\left(x\right)\ =\ 2x-4$
$g\left(x\right)\ =\ 2^x\ -\ 4$
$h\left(x\right)=\left(\frac{1}{2}\right)^x\ -\ 4$
$k\left(x\right)\ =\ \frac{1}{2}x-4$

a)

$f\left(x\right)$ and $k\left(x\right)$ are linear.

b)

$g\left(x\right)$ is exponential growth.

c)

$h\left(x\right)$ is exponential decay.

d)

$f\left(x\right)\ and\ g\left(x\right)$ are both exponential growth.

e)

$h\left(x\right)\ and\ k\left(x\right)$ are both exponential decay.

5.

Is this equation exponential growth, decay, or neither?

a)

Exponential Growth

b)

Exponential Decay

c)

Neither

6.

Is this exponential growth or decay?

a)

Growth

b)

Decay

7.

Is this exponential growth or decay?

a)

Growth

b)

Decay

8.

Pick the equation that is exponential growth:

a)

y=2(0.5)^x

b)

y = 0.5(2)^x

9.

If a table's pattern is that the f(x) values are being divided by -3, what is the common ratio?

a)

3

b)

-3

c)

$\frac{1}{3}$

d)

$-\frac{1}{3}$

10.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

11.

What is the X-INTERCEPT of the exponential function?

a)

(0,1)

b)

(0,0)

c)

There is not one.

12.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y = 8(15,000)^x

b)

y = 15,000(1.08)^x

c)

y = 15,000(0.92)^x

d)

y = 15,000(0.08)^x

13.

A new savings account is opened with $400 and earns 3% interest per year. What is the exponential function?

a)

f(x) = 400(3)^x

b)

f(x) = 400(0.97)^x

c)

f(x) = 400(1.03)^x

d)

f(x) = 400(0.03)^x

14.

An adult takes 800 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%.

Write an equation to represent the function. Then, use the function to find out how much ibuprofen is left after 6 hours?

a)

101 mg

b)

102 mg

c)

103 mg

d)

104 mg

15.

Which of the equations below represent this table of values?

a)

y = 3(36)^x

b)

y = 36(3)^x

c)

y = 3(⅓)^x

d)

y = 36(⅓)^x

16.

Daniel purchased a car for $35,000. Each year, his car depreciates at a rate of 5%.

Write a function, and use it to figure out how much will the car be worth in 8 years.

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

17.

What is the y-intercept of the function?

a)

(0, 2)

b)

(0, 3)

c)

(0, 1)

d)

(0, -2)

18.

What is the y-intercept of the function?

f(x) = 2(4)^x

a)

(0, 2)

b)

(0, 4)

c)

(0, 8)

d)

(0, $\frac{1}{2}$ )

19.

What is the percent of increase in this function?

f(x) = 300(1.16)^x?

a)

16%

b)

1.16%

c)

300%

d)

84%

20.

In an exponential function, what does the 'a' represent?

a)

slope

b)

input

c)

y-intercept

d)

common ratio

e)

output

21.

Sabra opened an savings account that earns interest each year. The equation y = 5000(1.01)^x represents the account balance, y, of the account that was open for x years.

What is the interest rate on Sabra's account?

a)

1.01%

b)

99%

c)

1%

d)

0.01%

22.

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 8% per minute.

Which decay rate would be used in the function?

a)

1.92

b)

1.08

c)

0.08

d)

0.92

23.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

24.

Write the explicit formula for the geometric sequence.

a)

$a_n=4\cdot(3)^{n-1}$

b)

$a_n=3\cdot(4)^{n-1}$

c)

$a_n=-4\cdot(3)^{n-1}$

d)

$a_n=3\cdot(-4)^{n-1}$

25.

Find the first four terms of the sequence given the rule:

$a_n=4\cdot(5)^{n-1}$

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

26.

What is the 14th term of the geometric sequence?

**HINT: Write the explicit formula and use it to help you!**

a)

14,348,907

b)

4,782,969

c)

1,594,323

d)

45

27.

Select all the TRUE statements about the function below:

$a_n=10\cdot(2)^{n-1}$

a)

The common ratio of the function is 2.

b)

The first term of the sequence is 20.

c)

The third term of the sequence is 40.

d)

$a_1$ is 10.

e)

If graphed, this sequence would show exponential decay.

28.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n=a_n-1+11
a₁=6

b)

a_n=a_n-1-4
a₁=6

c)

a_n=a_n-1+9
a₁=6

d)

a_n=a_n-1+6
a₁=6

29.

Find the common ratio: 64, -16, 4, -1, ...

a)

r = $\frac{1}{4}$

b)

r = $-\frac{1}{4}$

c)

r = -4

d)

r = 4

30.

Select all the TRUE statements about the sequence:

10, 5, 0, -5,...

a)

The recursive formula is:
$a_1=10\ \ ,\ \ a_n=a_{n-1}-5$

b)

$a_n=10\cdot\left(5\right)^{n-1}$
is the explicit formula.

c)

The explicit formula is $a_n=10+\left(n-1\right)\left(-5\right)$

d)

The common difference is -5.

e)

The common ratio is -5.

Exponential Functions and Geometric Sequences

Total questions: 30

Worksheet time: 2hrs 19mins

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