SAT Math: Exponential Growth and Decay Practice Questions
Interpret exponential factors, calculate repeated growth or decay, and connect a model to its time unit. Try each original question before checking its worked explanation. This focused practice is free and requires no account.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. A culture starts with 300 cells and increases by 50% each hour. How many cells does the model predict after 2 hours?
Explanation. A 50% increase multiplies the current count by 1.5. Two hours give 300(1.5)^2 = 300(2.25) = 675. Adding the same 150 twice would model linear rather than repeated percentage growth.
2. A machine is worth $500 initially and loses 10% of its current value each year. What is its modeled value after 2 years, in dollars?
Explanation. Retaining 90% each year means multiplying by 0.9 twice: 500(0.9)^2 = 405. The second year's decrease is 10% of 450, so it is $45.
3. The model P(t) = 80(1.25)^t gives a population after t years. What is the annual percentage increase?
Explanation. A growth factor has the form 1 + r. Here r = 1.25 - 1 = 0.25, which is 25%. The initial population 80 does not change the percentage rate.
4. A quantity starts at 160 and doubles every 3 hours. What is its value after 9 hours?
Explanation. Nine hours contain 9/3 = 3 doubling periods. Multiply the initial value by 2^3: 160(8) = 1280.
5. A sample follows M(t) = 96(1/2)^(t/4), where t is measured in days. How many days does it take for the modeled mass to decrease from 96 to 24?
Explanation. The ratio 24/96 is 1/4 = (1/2)^2. Therefore t/4 = 2 and t = 8 days. Two half-life periods reduce the mass to one fourth.
6. A model has values f(0) = 7, f(1) = 21, and f(2) = 63, and multiplies by the same positive factor for every increase of 1 in x. What is f(4)?
Explanation. The common factor is 21/7 = 63/21 = 3. From x = 2 to x = 4 there are two more multiplications, so f(4) = 63(3)(3) = 567.
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FAQ
How do growth and decay factors differ?
A positive factor greater than 1 represents growth. A factor between 0 and 1 represents decay. Match the exponent to the number of time periods.
How can a table distinguish linear from exponential growth?
Equal differences for equal input steps indicate a linear pattern. Equal positive ratios indicate an exponential pattern.