AnswersHigh School Math 2 AGeometric Sequences

Geometric Sequences — Unit test Answers

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A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

A
2.5 days
B
5.0 days
C
46.6 days
D
66.7 days
2
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Yui makes a list of the balances in her savings account at the end of each month. She notices that each month’s total is 5% greater than the previous month’s total. She writes a recursive formula to describe the account balances.

A
0.05
B
0.5
C
1.05
D
5.0
3

The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?Plant Heightt, time in monthsh, height in inches118218.21318.33418.42518.48618.54

A
10 months
B
14 months
C
16 months
D
28 months
4

What is the common ratio of the sequence?-2, 6, -18, 54,...

A
−3
B
−2
C
3
D
8
5

Which of the following describes the growth rate of the exponential function in the graph below?

Question illustration
A
For each x increase of 1, the y increases by a common difference of 3.
B
For each x increase of 1, the y increases by a common factor of 3.
C
For each x increase of 1, the y increases by 4 more than the previous increase.
D
For each x increase of 1, the y increases by doubling and then adding 1.
6

What is the solution to the equation

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

Tables of values for two different functions are given below. Which statement is true?

Question illustration
A
The right function grows approximately 21 times faster than the left function over the interval 4 < x < 5.
B
The right function grows approximately 21 times slower than the left function over the interval 4 < x < 5.
C
The right function grows approximately 6 times faster than the left function over the interval 2 < x < 3.
D
The right function grows approximately 2.5 times slower than the left function over the interval 2 < x < 3.
8

What is the true solution to the equation below?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
9

An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?

A
3.3 years
B
5.0 years
C
5.6 years
D
6.6 years
10

Ajay analyzed two companies and has formulated tables to model each company’s growth, where x represents the age of the companies in years and y represents growth in terms of number of employees. Company 1 Company 2 If the number of employees is an indicator of a successful business, in which company should Ajay invest?

Question illustration
A
company 1 because it is adding six employees each year while company 2 is multiplying its number of employees by six each year
B
company 1 because it is multiplying its number of employees by six each year while company 2 is adding six employees each year
C
company 2 because it is adding six employees each year while company 1 is multiplying its number of employees by six each year
D
company 2 because it is multiplying its number of employees by six each year while company 1 is adding six employees each year
11

Which graph is the sequence defined by the function f(x) = 3(2)x-1?

A
On a coordinate plane, 5 points are plotted. The points are (0, 2), (1, 6), (2, 18), (3, 54), (4, 162).
Option A
B
On a coordinate plane, 5 points are plotted. The points are (1, 2), (2, 6), (3, 18), (4, 54), (5, 162).
Option B
C
On a coordinate plane, 6 points are plotted. The points are (0, 3), (1, 6), (2, 12), (3, 24), (4, 48), (5, 96).
Option C
D
On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Option D
12

Which equation describes the relationship between the variables in the table below?xy-11928146,561559,049

Question illustration
A
; each y-value is the previous y-value multiplied by 9.
Option A
B
; each y-value is the previous y-value plus 9 more than was added previously.
Option B
C
; each y-value is the previous y-value plus 9.
Option C
D
; each y-value is the previous y-value multiplied by another 9.
Option D
13

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has $658.80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613.04. What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

A
Makayla invests her money 1 year longer.
B
Makayla invests her money 2 years longer.
C
Calvin invests his money 1 year longer.
D
Calvin invests his money 2 years longer.
14

1.2, 3, 7.5, 18.75, ...

A
f(x) = 1.2(2.5)x – 1
B
f(x) = 2.5(1.2)x – 1
C
f(x) = 1.2(2.5)x
D
f(x) = 2.5(1.2)x
15

What is the solution to the equation below?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
16

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.

Question illustration
A
1 year
B
2 years
C
5 years
D
8 years
17

The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A scientist has a 10-mg sample of a radioactive isotope. The isotope has a half-life of 8 days. After 16 days, how much of the radioactive isotope remains?

Question illustration
A
2.0 mg
B
2.5 mg
C
5.7 mg
D
7.1 mg
18

Select two options.

A
The graph will show exponential growth.
B
The graph will appear linear.
C
The domain will be the set of natural numbers.
D
The range will be the set of natural numbers.
E
The graph will show exponential decay.
19

Isaak is writing an explicit formula to represent the sequence.64, 112, 196, 343, ...What value should he use as the common ratio in the formula? Write the answer as a decimal rounded to the nearest hundredth.

A
0.75
B
1.75
C
58
D
279
20

A linear function and an exponential function are shown below. Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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