SAT Math Practice Test: Exponential Functions
- Exponential Functions and Growth
- 10 questions
- 15 minutes
These 10 questions practice exponential models from the SAT Advanced Math domain. Turn every percent change into a growth factor first: a 5% increase means multiply by 1.05, a 12% decrease means multiply by 0.88.
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Question 1
A town had 2,400 residents at the start of a study, and its population increased by 5% each year. Which function gives the population P of the town t years after the start of the study?
Correct answer: B
Each year the population is multiplied by 1 + 0.05 = 1.05, so P(t) = 2,400(1.05)t. The factor 0.05 would shrink the population by 95% each year.
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Question 2
A car was bought for $18,000. Its value decreases by 12% each year. What is the value of the car 2 years after it was bought?
Correct answer: B
The value after 2 years is 18,000(0.88)² = $13,939.20. The choice $13,680.00 subtracts 24% at once, which ignores that the second 12% is taken from a smaller value.
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Question 3
f(x) = 3 · 2x
For the function f shown, what is the value of f(4)?
Correct answer: B
The exponent applies only to 2: f(4) = 3 · 24 = 3 · 16 = 48. The choice 1,296 comes from computing (3 · 2)4, and 24 from 3 · 2 · 4.
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Question 4
A medicine sample contains 80 milligrams of a substance with a half-life of 6 hours. How many milligrams of the substance remain after 24 hours?
Correct answer: A
24 hours is 4 half-lives, so the amount is 80 · (1/2)4 = 5 milligrams. The choice 10 is the amount after 18 hours, or 3 half-lives.
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Question 5
f(x) = 500(0.93)x
Which statement best describes how the value of f(x) changes?
Correct answer: C
A growth factor of 0.93 is less than 1, so the value keeps 93% each step and loses 7%. The choice "decreases by 93%" confuses the part kept with the part lost.
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Question 6
A colony of 200 bacteria triples every 4 hours. Which function gives the number of bacteria N after t hours?
Correct answer: D
The colony triples once per 4 hours, so the exponent counts 4-hour periods: t/4. Check: at t = 8, 200 · 3² = 1,800, which is two triplings. The exponent 4t would mean 4 triplings every hour.
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Question 7
Which expression is equivalent to 50(1.2)2t?
Correct answer: A
By the power rule, (1.2)2t = ((1.2)²)t = (1.44)t. The choice 50(2.4)t multiplies 1.2 by 2 instead of squaring it.
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Question 8
x 0 1 2 3 y 5 15 45 135 Which equation fits all the values in the table?
Correct answer: C
Each y-value is 3 times the one before, and y = 5 when x = 0, so y = 5 · 3x. The equation y = 10x + 5 fits the first two points only (it gives 25, not 45, at x = 2).
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Question 9
Ana deposits $1,000 in a savings account that earns 4% interest compounded once a year. She makes no other deposits or withdrawals. To the nearest cent, how much is in the account after 3 years?
Correct answer: C
The balance is 1,000(1.04)³ = $1,124.86. The choice $1,120.00 is simple interest (3 × $40 added), which ignores interest earned on earlier interest.
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Question 10
9x = 27x − 1
What value of x satisfies the equation shown?
Correct answer: D
Write both sides as powers of 3: 32x = 33x − 3, so 2x = 3x − 3 and x = 3. The choice −3 comes from a sign error when moving 3x to the left side.
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