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SAT Math: Exponentials and Radicals (Drill 2)

Drill 2 · Math · Exponentials and Radicals

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About This Drill

SAT Math: Exponentials and Radicals (Drill 2) is a Math practice drill covering Exponentials and Radicals. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Exponential function questions on the SAT model growth and decay using equations of the form f(x) = ab^x. This drill covers compound interest, half-life applications, fractional exponents, and interpreting what the base and initial value represent in context.

Questions & Explanations

Question 1. An investor deposits $1,000 into an account that earns 5% interest compounded annually. A = 1,000(1.05)t. What is the amount after 2 years, to the nearest dollar?

  • A) $1,103 ✓
  • B) $1,100
  • C) $1,050
  • D) $1,150

Explanation: A = 1,000(1.05)2 = 1,000(1.1025) = $1,102.50, rounds to $1,103. Choice B is simple interest.

Question 2. What is the value of 4−3/2?

  • A) −8
  • B) 1/4
  • C) 1/8 ✓
  • D) −1/8

Explanation: 4−3/2 = 1/43/2. 41/2 = 2, then 23 = 8. So 1/8. Negative exponents don't make the result negative.

Question 3. A radioactive substance has a half-life of 6 hours. If a sample initially contains 800 mg, how many mg remain after 18 hours?

  • A) 200
  • B) 100 ✓
  • C) 50
  • D) 400

Explanation: 18/6 = 3 half-lives. 800 → 400 → 200 → 100.

Question 4. What is the value of 272/3?

  • A) 3
  • B) 6
  • C) 18
  • D) 9 ✓

Explanation: Cube root of 27 = 3. Then 32 = 9.

Question 5. The population of a city is modeled by P(t) = 50,000(0.97)t. Which statement best describes the trend?

  • A) The population decreases by 3% per year. ✓
  • B) The population increases by 3% per year.
  • C) The population decreases by 97% per year.
  • D) The population increases by 97% per year.

Explanation: 0.97 = 1 − 0.03, so the population decreases by 3% per year.