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Exponential Growth Functions Answers

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1
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Which statements could he include in his explanation? Select two options.

A
The domain of both functions is all real numbers.
B
The domain of f(x) is x > 5.
C
The domain of g(x) is x > 5.
D
The range of f(x) is y > 0.
E
The range of g(x) is y > 0.
2
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Several ordered pairs from a continuous exponential function are shown in the table.

Question illustration
A
The domain is the set of integers, and the range is y > 4.
B
The domain is the set of integers, and the range is y > 0.
C
The domain is the set of real numbers, and the range is y > 0.
D
The domain is the set of real numbers, and the range is y > 4.
3

Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?

A
On a coordinate plane, the point (0, 3) is graphed.
Option A
B
On a coordinate plane, the point (0, 4) is graphed.
Option B
C
On a coordinate plane, the point (3, 0) is graphed.
Option C
D
On a coordinate plane, the point (4, 0) is graphed.
Option D
4

A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)

A
y = 18(1.15)x
B
y = 18(0.15)x
C
y = 20.7(1.15)x
D
y = 20.7(0.15)x
5

Which graph shows exponential growth?

A
On a coordinate plane, a parabola opens up with vertex at (0, 0).
Option A
B
On a coordinate plane, a curve approaches y = 0 in quadrant 2 and curves up into quadrant 1.
Option B
C
On a coordinate plane, a straight line with positive slope crosses the y-axis at (negative 1, 0) and crosses the y-axis at (2, 0).
Option C
D
On a coordinate plane a curve opens down and to the right in quadrants 1 and 4. It crosses the x-axis at (1, 0).
Option D
6

An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made, which graph can be used to determine approximately how many years will it take for the balance to be $282?

A
Option
B
Option
C
Option
D
Option
7

Which is the graph of f(x) = 5(2)x?

A
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 5) and (2, 20).
Option A
B
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 2) and (2, 50).
Option B
C
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 2) and (2, 10).
Option C
D
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 5) and (2, 10).
Option D
8

Which is the graph of f(x) = 0.5(4)x?

A
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 1), (2, 8), (3, 32).
Option A
B
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 4), (1, 16), (2, 64).
Option B
C
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 1), (3, 8), (4, 16).
Option C
D
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 1), (1, 8), (2, 32).
Option D
9

A function of the form f(x) = abx is modified so that the b value remains the same but the a value is increased by 2. How do the domain and range of the new function compare to the domain and range of the original function? Check all that apply.The range stays the same. The range becomes y > 2.The domain stays the same. The domain becomes x > 2.The range becomes y ≥ 2.The domain becomes x ≥ 2.

A
The range stays the same.
B
The range becomes y > 2.
C
The domain stays the same.
D
The domain becomes x > 2.
E
The range becomes y ≥ 2.
F
The domain becomes x ≥ 2.
10

A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation?

A
y = 1,000(1.15)6; 2,313 bacteria
B
y = 1,000(1.15)7; 2,660 bacteria
C
y = 1,000(1.5)5; 7,594 bacteria
D
y = 1,000(1.5)6; 11,391 bacteria

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