Precalculus Practice Test: Exponential Functions
- Exponential Functions
- 10 questions
- 15 minutes
These 10 questions cover exponential growth and decay, compound and continuous interest, doubling time and equations with the same base. In y = a·bx, a base b above 1 means growth and a base between 0 and 1 means decay.
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Question 1
If f(x) = 3·2x, what is f(4)?
Correct answer: C
Evaluate the power first: 24 = 16, and 3·16 = 48. The value 1,296 = 64 comes from multiplying 3 and 2 before raising to the power.
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Question 2
Which function models exponential decay?
Correct answer: A
The base 0.85 is between 0 and 1, so the value shrinks by 15% each period. In y = 0.85(2)t the starting value is small, but the base 2 still makes it grow.
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Question 3
A deposit of $2,000 earns 5% interest compounded annually. What is the balance after 3 years, to the nearest cent?
Correct answer: D
The balance is 2000(1.05)3 = 2000(1.157625) = $2,315.25. The amount $2,300.00 is simple interest, which ignores interest earned on interest.
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Question 4
What is the solution of 4x + 1 = 8x?
Correct answer: B
Write both sides with base 2: 22x + 2 = 23x, so 2x + 2 = 3x and x = 2. Check: 43 = 64 = 82.
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Question 5
What is the horizontal asymptote of y = 2x − 5?
Correct answer: C
The term 2x approaches 0 as x → −∞, so y approaches 0 − 5 = −5. The asymptote y = 0 belongs to y = 2x before the shift down.
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Question 6
A bacteria culture starts with 400 cells and doubles every 6 hours. How many cells are there after 24 hours?
Correct answer: A
Twenty-four hours contain 4 doubling periods, so the count is 400·24 = 6,400. The value 3,200 counts only 3 doublings.
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Question 7
An account starts with $1,000 and earns 4% interest compounded continuously, so A = 1000e0.04t. What is the balance after 10 years, to the nearest cent?
Correct answer: B
The balance is 1000e0.4 ≈ 1000(1.49182) = $1,491.82. The amount $1,480.24 is annual compounding, 1000(1.04)10, which grows slightly less.
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Question 8
An exponential function y = a·bx passes through (0, 5) and (2, 45). Which function is it?
Correct answer: D
The point (0, 5) gives a = 5, and 5b2 = 45 gives b2 = 9, so b = 3. The base 9 forgets to take the square root.
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Question 9
The value of a car is modeled by V = 24,000(0.92)t, where t is in years. How does the value change each year?
Correct answer: C
Each year the value is multiplied by 0.92 = 1 − 0.08, so it keeps 92% and loses 8%. The 92% is what remains, not what is lost.
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Question 10
Which expression is equivalent to e2x·ex − 3?
Correct answer: A
When powers with the same base are multiplied, the exponents are added: 2x + (x − 3) = 3x − 3. Multiplying the exponents gives 2x2 − 6x, which is the rule for a power of a power.
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