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Exponential Functions Practice Questions

SAT · SAT Math · 148 free MCQs with instant results and detailed explanations.

148
Total
39
Easy
90
Medium
19
Hard

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Sample Questions from Exponential Functions

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Q1
Easy
What is the value of 2^3?
A. 6
B. 8
C. 4
D. 2
Show Answer & Explanation
Correct Answer: B
2^3 means 2 multiplied by itself 3 times: 2 × 2 × 2 = 8.
Q2
Easy
Which of the following represents an exponential growth function?
A. y = 5x
B. y = 2^x
C. y = x^2
D. y = 10 + x
Show Answer & Explanation
Correct Answer: B
y = 2^x shows exponential growth because it increases rapidly as x increases, unlike linear or polynomial functions.
Q3
Easy
What is the value of 2^5?
A. 8
B. 16
C. 32
D. 64
Show Answer & Explanation
Correct Answer: C
2 raised to the power of 5 equals 32, as 2 * 2 * 2 * 2 * 2 = 32.
Q4
Medium
If the function f(x) = 3^(x + 2) represents an exponential growth model, what is the value of f(1)?
A. 27
B. 9
C. 81
D. 12
Show Answer & Explanation
Correct Answer: A
To find f(1), substitute x = 1 into the function: f(1) = 3^(1 + 2) = 3^3 = 27.
Q5
Medium
The population of a certain bacteria doubles every 3 hours. If the initial population is 250, what will be the population after 9 hours?
A. 2000
B. 1500
C. 1000
D. 750
Show Answer & Explanation
Correct Answer: A
After 9 hours, the population will have doubled 3 times (9/3 = 3). Therefore, 250 * 2^3 = 250 * 8 = 2000.
Q6
Medium
Which of the following equations represents an exponential decay model with a base of 0.5 after time t?
A. y = 100(0.5)^t
B. y = 100(2)^t
C. y = 50(0.5)^t
D. y = 100(0.1)^t
Show Answer & Explanation
Correct Answer: A
An exponential decay model has a base between 0 and 1. The correct equation y = 100(0.5)^t shows decay with a starting value of 100.
Q7
Medium
If the exponential function f(x) = a * 2^(bx) represents a growth model, which of the following conditions must be true for a and b?
A. a > 0 and b > 0
B. a < 0 and b > 0
C. a > 0 and b < 0
D. a < 0 and b < 0
Show Answer & Explanation
Correct Answer: A
For an exponential growth model, both a and b must be positive; otherwise, the function would not exhibit growth.
Q8
Hard
The population of a certain bacteria doubles every 3 hours. If the initial population is 500, what will be the population after 12 hours?
A. 8000
B. 3000
C. 6000
D. 2000
Show Answer & Explanation
Correct Answer: A
After 12 hours, the bacteria have doubled 4 times (12 hours / 3 hours = 4). Therefore, the population is 500 * 2^4 = 500 * 16 = 8000.
Q9
Hard
A population of bacteria grows exponentially according to the model P(t) = P_0 * e^(kt), where P_0 is the initial population, k is a positive constant, and t is time in hours. If the population triples in 4 hours, what is the value of k?
A. 0.25 ln(3)
B. 0.75 ln(3)
C. 0.5 ln(3)
D. 1.5 ln(3)
Show Answer & Explanation
Correct Answer: A
To find k, we set P(4) = 3P_0. Thus, 3P_0 = P_0 * e^(4k). Dividing by P_0 and solving gives k = (1/4) ln(3).
Q10
Hard
A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours?
A. 2000
B. 4000
C. 8000
D. 10000
Show Answer & Explanation
Correct Answer: C
The population doubles every 3 hours. After 12 hours, which is 4 doubling periods (12/3 = 4), the population will be 500 * 2^4 = 500 * 16 = 8000.

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Exponential Functions — SAT SAT Math Practice Questions Online

This page contains 148 practice MCQs for the chapter Exponential Functions in SAT SAT Math. The questions are organized by difficulty — 39 easy, 90 medium, 19 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.