Free Printable Review 7.5-7.8

Worksheets

Review 7.5-7.8

Total questions: 48

Worksheet time: 3hrs 44mins

Name

Class

Date

Write the explicit formula for the following geometric sequence:

10, 20, 40, 80, ...

a_n = 10(2)^n-1

a_n = 2(10)^n-1

a_n = 10(2)ⁿ

a_n = 2(10)ⁿ

Write the explicit formula for the following geometric sequence:

100, 50, 25, 12.5, ...

a_n = 2(100)^n-1

a_n = 100(2)^n-1

a_n = 100(1/2)^n-1

a_n = (1/2)(100)^n-1

Write the explicit rule for the following geometric sequence:

2, -12, 72, ...

a_n = 72(-6)^n-1

a_n = 2(-6)^n-1

a_n = 2(6)^n-1

a_n = 72(-6)^n-1

Write the explicit formula for the following geometric sequence:

3, -12, 48, -192, ...

a_n = 4(3)^n-1

a_n = 3(4)^n-1

a_n = -4(3)^n-1

a_n = 3(-4)^n-1

Is the table linear, exponential or neither?

Linear

Exponential

Neither

Which equation is represented by the table?

y = 40(2)^x

y = 40(1/2)^x

y = 40 - 2x

y = 40 - 1/2x

Which table represents the following equation?

Which equation is represented by the table?

$y=\frac{1}{8}\left(2\right)^x$

$y=\frac{1}{8}\left(\frac{1}{2}\right)^x$

$y=2^x$

$y=2\left(2\right)^x$

Which table represents the following equation?

10.

Which function is best represents

f(x)=2(5)^x

11.

Which equation best describes the graph?

y = 2^x + 4

y = 2^x - 3

y = 2^x - 4

y = 2^x + 3

12.

Write the equation of the graph.

f(x) = -3^x- 2

f(x) = -3^x + 2

f(x) = 3^x + 2

f(x) = 3^-x + 2

13.

Which graph corresponds to the exponential function $y=-4^x$ ?

14.

Which equation matches this graph?

15.

North Dakota has recently had the fastest growing population out of all 50 states. On Jan 1, 2013, the population of North Dakota was 700,000 people. North Dakota’s population has been growing by 5% per year. Express North Dakota’s population, N, in terms of years since 2013, t.

Check the BEST answer:

N=700,000(1.05)t

N=700,000(1.5)t

N=700,000(1-0.05)^t

N=700,000(0.95)^t

16.

An air freshener starts with 30 grams of fluid, and the amount of fluid decreases by 12% per day. Express the amount of grams of freshener, Q, that remains, t, days after it has begun being used.

Check the BEST answer: (HINT: that means simplify what is in the parenthesis)

Q=30(1+0.12)^t

Q=30(1-0.12)^t

Q=30(0.88)^t

Q=12(1.30)^t

17.

Middletown High School has student elections every year. Lately, the school has seen a 5% decrease in voting from election to election. If 910 students voted this year, how many will be expected to vote 8 years from now? (Round to the nearest whole number if necessary).

604

777

198

18.

More and more people are purchasing food from farmers' markets. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 15% each year. If there are 6,200 farmers' markets this year, how many will there be in 10 years? (Round to the nearest whole number if necessary).

25,082

12,937

62,000

43,511

19.

The population of a small town is 1600 and is increasing at a rate of 3% per year. Write an exponential function to model this situation. Then find the population of the town after 10 years. (Verbal Question: How do we know this is growth or decay?)

f(t) = 1600(1.03)^t; 2,150 people

f(t) = 1600(0.97)^t; 1,738 people

f(t) = 1600(1.03)^t; 2,128 people

f(t) = 1600(0.97)^t; 1,819 people

20.

The value of a book is $58 and depreciates at a rate of 7% per year. Write an exponential function to find the value of the book after 8 years. (Verbal Question: How do we know this is growth or decay?)

f(t) = 58(0.93)^t; $32.46

f(t) = 58(1.07)^t; $76.32

f(t) = 58(0.93)^t; $34.26

f(t) = 58(1.07)^t; $73.62

21.

Find the balance in the account after the given period.

$5000 deposit earning 1.5% compounded quarterly after 3 years

$5,229.70

$7,604.38

$7,777.27

$5,538.86

22.

Find the balance in the account after the given period.

$13,500 deposit earning 3.3% compounded monthly after 1 year

$13,611.38

$14,898.84

$13,537.13

$13, 952.30

23.

Your 6 year investment of $40,000 at 14% compounded quarterly is worth how much now?

$928,488.27

$49,170.21

$91,333.14

$51,333.14

24.

Will deposits $1650 for three years at 3% interest, compounded daily. What is his ending balance?

$1,700.25

$4,056.85

$2,103.87

$1,805.38

25.

Jamere deposits $2350 in an account that earns interest at a rate of 3.1%, compounded monthly. What is his ending balance after five years?

$2743.98

$2,743.45

$2,362.01

$10,856.16

26.

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

-16, -21, -26, -31

5, -11, -27, -43

-16, -80, -500, -200

-16, -11, -6, -1

27.

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1- 1

28.

Find the first four terms of the sequence.

a_n= 2a_(n-1)+ n where a₀= 0

0, 0, 0, 0

0, 1, 4, 11

0, 1, 2, 4

0, 2, 4, 8

29.

If 10 mg of iodine 131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.

1.25mg

1.25g

10g

10mg

30.

The half-life of strontium-90 is 25 years. How much strontium-90 will remain after 100 years if the initial amount is 4.0 g?

3.0g

0.25mg

0.3g

0.25g

31.

The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how many grams would be left after 7.2 minutes has elapsed?

100.0g

50.0g

12.5g

8.5g

32.

Find the 9th term in the following geometric sequence:

4, 8, 16, 32, ...

384

512

768

1,024

33.

What is the 14th term of the geometric sequence?

14,348,907

4,782,969

1,594,323

34.

Find a₁₂ in the sequence -1, -3, -9, -27, ...

-177,147

-19,683

-59,049

118,098

35.

A geometric sequence has a common ration(r) of 3 and the 8th term (a₈) is 13,122. What is the first term of the sequence (a₁)?

36.

A geometric sequence has a common ration(r) of 2 and the 13th term (a₁₃) is 36,864. What is the first term of the sequence (a₁)?

37.

A publishing industry report predicts that magazine subscriptions will drop by 10% each year. If this prediction is correct, then how many subscribers will a magazine with 98,000 subscribers have in 10 years? (Round to the nearest whole number if necessary).

34,170

16,348

7690

76,023

38.

A cliff overlooking Oak Grove Lake is experiencing erosion, losing elevation at a rate of 5% every millennium. The cliff's current elevation is 1,200 meters. What will its elevation be in 6 millennia? (Round to the nearest whole number if necessary).

882

465

349

975

39.

What is the equation of the horizontal asymptote for following exponential function?

y = -4

y > -4

y < -4

(0, -3)

40.

What is the horizontal asymptote for y = 2^x - 3

y = 0

y = -3

x = 0

x = -3

41.

What is the asymptote?

y=0

x=2

y=1

x=0

42.

What is the horizontal asymptote?

y=3

y=-2

y=-3

(0,-3)

43.

What is the range of this graph?

y = 6

(0, -4)

y > -6

y < -6

44.

What is the range of this function?

(-∞,0)

(0,∞)

(-∞,4)

(4,∞)

45.

What is the range of f(x) = 5^x?

-∞ ≤ x ≤ ∞

-∞ ≤ y ≤ ∞

x > 0

y > 0

46.

625, 375, 225, 135

What is the common ratio r?

(a)

47.

a₁=54 & a₃=6

What is the common ratio r?

-3

-12

$\frac{1}{3}$

48.

a₂=6 & a₄=54

What is the common ratio r?

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Review 7.5-7.8

Total questions: 48

Worksheet time: 3hrs 44mins

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