Free Printable A1 Test 7: Exponential Functions & Geometric Seq OPTIONAL Review

1.

What is it about the equation y = 2(9/7)^x that indicates that it is a model for exponential growth?

a)

The equation is growth because 2 is positive.

b)

The equation is growth because the factor is positive.

c)

The equation is growth because the factor is greater than one.

d)

The equation is growth because the exponent is always positive.

2.

Consider the equation y=200(1.08)^x which models the increase in value of an autographed Annie program. Let y = the value of the item, let x = the number of years since the performance. What does the 1.08 in the equation indicate?

a)

The value of the item is increasing by $1.08 each year.

b)

The value of the item is increasing by 1.08% each year.

c)

The value of the item will increase to $200 1.08 years after purchase.

d)

The value of the item is increasing by 8% each year.

3.

A population of mutant venus fly trap plants are taking over an island in the South Pacific, capturing everything from insects to small rodents. When they were first discovered they covered 4 square kilometers. As the population grows, the plants spread and cover more land. Use the table to write an equation.

a)

y=4(4)^x

b)

y=4(2.68)^x

c)

y=4(1+1.67)^x

d)

y=4(1.67)^x

4.

A population of mutant venus fly trap plants are taking over an island in the South Pacific, capturing everything from insects to small rodents. When they were first discovered they covered 4 square kilometers. As the population grows, the plants spread and cover more land. How many years will it take for the plants to occupy 400 km²?

a)

8 years

b)

9 years

c)

10 years

d)

11 years

5.

You are sick and your doctor prescribes a medication. One dose is 200 mg. Every half hour 30% of the medication leaves the body. You take the first dose at 6 am. If y = amount of medication in the body and x = a 30 minute interval, what equation fits the scenario?

a)

y=30(0.70)^x

b)

y=200(0.30)^x

c)

y=200(x)^0.3

d)

y=200(0.70)^x

6.

If you are given the following tables, how would you fill in the missing values?

a)

Find the common difference for the linear table and use that to find the other y values and for the exponential table find the first difference and use that to find the other y values.

b)

Use the second difference to find the linear table values and the third difference to find the exponential table values.

c)

Find the first difference for the linear table and use that to find the other y values and for the exponential table find the common ratio and use that to find the other y values.

d)

Give up.

7.

What parts of a linear equation could you find in a table?

a)

The slope is found as the first difference in the table, and the y-intercept is where y=0.

b)

The slope is found as the common ratio in the table, and the y-intercept is where x = 0.

c)

The slope is found as the common ratio in the table, and the y-intercept is where y = 0.

d)

The slope is found as the first difference in the table, and the y-intercept is where x=0.

8.

Match the following

a)

1.

Growth

b)

2.

Decay

c)

a

3.

y-intercept

d)

$y\ =\ ab^x$

4.

Exponential Function Equation

e)

b

5.

Growth/Decay Factor

9.

Describe the function. $y\ =\ 5^x$

a)

Growth

b)

Deacy

10.

Describe the function. $y\ =\ 2\left(\frac{1}{2}\right)^x$

a)

Growth

b)

Deacy

11.

The graph for an exponential function is called a (a)

Choose from the below words

curve

line

parabola

12.

What is the "a" or y-intercept of the function?

a)

2

b)

$\frac{1}{2}$

c)

1

13.

What is the Growth Factor of the equation.

$y\ =\ 5\left(3\right)^x$

14.

What is the "a" or y-intercept of the equation.

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

15.

Describe the function.

a)

Exponential Growth

b)

Exponential Decay

c)

Quadratic

16.

Describe the function.

a)

Exponential Growth

b)

Exponential Deacy

c)

Positive Linear

17.

Describe the function.

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

18.

a)

Exponential Growth

b)

Exponential Decay

c)

Quadratic

19.

Describe this function.

a)

Exponential Growth

b)

Exponential Decay

c)

Linear Positive

20.

In an exponential function, what does the 'a' represent?
f(x) = a ⋅ b^x

a)

A
Slope

b)

B
y -intercept

c)

C
x-intercept

d)

D
Common Ratio

21.

In an exponential function, what is an interpretation of the y-intercept?

a)

A
initial amount

b)

B
ending amount

c)

C
growth factor

d)

D
decay factor

22.

Which function will show exponential behavior?
f(x) = (4.3)^xg(x) = 4.3x + 9

a)

A
f(x)

b)

B
g(x)

c)

C
both

d)

D
neither

23.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

24.

To earn as much interest as possible, you should open a savings account that earns ______ interest and has the _____ interest rate.

a)

compound; lowest

b)

simple ; lowest

c)

compound ; highest

d)

simple ; highest

25.

When calculating interest, the rate must be converted into a ____ before multiplying.

a)

fraction

b)

mixed number

c)

decimal

d)

integer

26.

A bank is offering 7% annual compound interest on a savings account. If you deposit $1,500, what will be the total amount of money in your savings account after three years?

a)

$337.56

b)

$1837.56

c)

$1663.08

d)

$1843.88

27.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years?

a)

$11,255.37

b)

$15,683.28

c)

$8.928.59

d)

$16,349.72

28.

Given an investment of $1,500:
Which investment would have a larger balance after 5 years?
Option 1 - 4% compounded monthly
Option 2 - 3.9% compounded daily.

a)

Option 1

b)

Option 2

29.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

30.

Find the common ratio for the geometric sequence.

a)

10

b)

1/2

c)

2

d)

4

31.

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

32.

Find the common ratio: 4, -16, 64, -256, ...

a)

r = -4

b)

r = 2

c)

r = -2

d)

r = 4

33.

What does a₁ represent?

a)

Any term

b)

First term

c)

Last term

34.

What does r represent?

a)

Radical

b)

Common difference

c)

Common ratio

35.

Find the next three terms: 4, 12, 36, 108, ...

a)

324, 972, 2916

b)

972, 2916, 8748

c)

405, 1215, 3645

36.

The next term of the geometric sequence

4, 16, 64, ... is

a)

256

b)

132

c)

120

d)

150

37.

What is the common ratio for the following sequence:

3, 15, 75, 375, ...

a)

12

b)

1/5

c)

5

d)

3

38.

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

a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

39.

What is a₅ in the sequence defined as follows?

a_n = 5 ⋅ 2^(n-1)

a)

a₅ = 160

b)

a₅ = 40

c)

a₅ = 10

d)

a₅ = 80

40.

To find the next term in a geometric sequence…

a)

add the common difference d

b)

multiply by the common ratio r

41.

Find the 5th term of the geometric sequence:

a)

10

b)

19

c)

1701

d)

567

42.

Find the common ratio for the geometric sequence.

a)

1

b)

-1

c)

7

d)

-7

43.

For each sequence, state if it is arithmetic, geometric, or neither.
−34, −26, −18, −10, −2, ...

a)

Arithmetic

b)

Geometric

c)

Neither

44.

Find the common ratio of the geometric sequence: -2, -4, -8, -16, . . .

a)

-2

b)

2

c)

4

d)

-4

45.

Is the sequence-4, -12, -36, -108,... arithmetic geometric, or neither?

a)

arithmetic

b)

geometric

c)

neither

46.

A geometric sequence models what type of function?

a)

linear

b)

quadratic

c)

exponential

d)

absolute value

47.

Find a₁₂ for the rule a_n = 6(2)^n-1

a)

4096

b)

24,576

c)

2048

d)

12,288

48.

Write the explicit rule for the geometric sequence:
2, -12, 72, ...

a)

a_n = 72(-6)^n-1

b)

a_n = 2(-6)^n-1

c)

a_n = 2(6)^n-1

d)

a_n = 72(-6)^n-1

49.

Carey is organizing her books and putting them on shelves. She put 2 books on the first shelf, 8 books on the second shelf, 32 books on the third shelf, and 128 books on the fourth shelf. What kind of sequence is this?

a)

Geometric

b)

Arithmetic

c)

Both

d)

Neither

50.

Find the explicit formula for the sequence shown in the graph.

a)

$a_n=32\left(\frac{1}{2}\right)^{\left(n-1\right)}$

b)

$a_n=32\left(2\right)^{\left(n-1\right)}$

c)

$a_n=\frac{1}{2}\left(32\right)^{\left(n-1\right)}$

d)

$a_n=32-16\left(n-1\right)$

A1 Test 7: Exponential Functions & Geometric Seq OPTIONAL Review

Total questions: 50

Worksheet time: 12hrs 2mins

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