SAT · Passport to Advanced Math · Exponential expressions and radicals
Question sat-q-00102
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The question
A town's population was 102 in 2020 and grew at a constant annual rate of 7% per year. Approximately what was the population 2 years later?
- 116
- 109
- 633
- 117
Show answer & worked solution
Answer: 117
Worked solution. Use exponential growth: y = a × b^t where a = 102, b = 1.07 (i.e., 1 + 7%), t = 2. So y = 102 × (1.07)^2 ≈ 117.
Why each wrong choice is wrong. The most common wrong answer treats the growth as linear (multiplying the rate by the years and adding). That underestimates the value because exponential growth compounds.
Test-day tactic. When the rate is 'per year' and applied 'each year', it's exponential. Use y = a × (1 + r)^t.
About this question type
Items test the laws of exponents (product, quotient, power, negative, fractional), simplifying radicals, and modelling exponential growth and decay using y = a·b^t. Compound-interest and half-life problems are extremely common.
You will see a question shaped like this one on roughly every other official SAT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.