Algebra 1 Practice Test: Exponential Growth and Decay
- Exponential Growth and Decay
- 10 questions
- 13 minutes
These 10 questions use models of the form y = a(1 + r)ᵗ and y = a(1 − r)ᵗ. A base greater than 1 means growth, and a base between 0 and 1 means decay.
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Question 1
In y = 500(1.04)t, what is the growth rate per time period?
Correct answer: D
The growth factor is 1 + r = 1.04, so r = 0.04, which is 4%. The factor 1.04 itself means 104% of the previous amount, not a 104% increase.
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Question 2
Which statement describes y = 800(0.85)t?
Correct answer: C
The base 0.85 is less than 1, so this is decay, and 1 − 0.85 = 0.15. Each period keeps 85% of the amount and loses 15%.
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Question 3
A population of 2,000 doubles every 3 years. What will the population be after 9 years?
Correct answer: A
Nine years is 3 doubling periods: 2000 · 23 = 16000. 6,000 comes from adding instead of doubling.
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Question 4
You deposit $1,000 at 5% interest compounded once a year. What is the balance after 3 years, to the nearest cent?
Correct answer: B
Use 1000(1.05)3 = 1157.625, which rounds to $1,157.63. $1,150.00 is simple interest, where interest is not earned on earlier interest.
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Question 5
Which function shows exponential decay?
Correct answer: D
Decay depends on the base, the number raised to the power x. Only y = 3(0.7)x has a base between 0 and 1; a small starting value like 0.7 does not make it decay.
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Question 6
A car worth $24,000 loses 12% of its value each year. Which function gives its value after t years?
Correct answer: A
Losing 12% means keeping 88%, so the decay factor is 1 − 0.12 = 0.88. Using 0.12 as the base would leave only 12% of the value each year.
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Question 7
The table shows an exponential function. Which equation matches it?
x 0 1 2 3 y 5 15 45 135 Correct answer: C
At x = 0 the value is 5, the initial amount, and each step multiplies by 3. y = 10x + 5 matches only the first two points.
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Question 8
A medicine dose of 80 mg has a half-life of 6 hours. How much remains after 18 hours?
Correct answer: B
18 hours is 3 half-lives: 80 → 40 → 20 → 10. Stopping after two halvings gives 20 mg.
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Question 9
What is the initial value of f(x) = 7(2)x?
Correct answer: A
The initial value is f(0) = 7 · 20 = 7 · 1 = 7. The 2 is the growth factor, and 14 is the value at x = 1.
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Question 10
A colony of 300 bacteria grows by 20% each hour. How many bacteria are there after 2 hours?
Correct answer: C
Multiply by 1.2 twice: 300(1.2)2 = 300 · 1.44 = 432. 420 adds 20% of the original 300 each hour, which is linear growth.
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