SAT Math
Nonlinear Functions
Nonlinear Functions is a skill in the Advanced Math domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.
14 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
The number of bacteria in a culture is modeled by the function N(h) = 500(1.2)^h, where h is the number of hours after the culture is started. In this context, what does the value 1.2 most likely represent?
- A. The population increases by exactly 1.2 bacteria every hour.
- B. It takes 1.2 hours for the population to double.
- C. The population grows by a factor of 1.2, or 20%, each hour. ✓
- D. The culture starts with 1.2 times as many bacteria as it did the previous hour.
Correct answer: C. In an exponential model of the form a(b)^h, the base b is the growth factor applied each time period; multiplying by 1.2 each hour represents 20% growth per hour.
The function g is defined by g(x) = −2(x − 3)² + 8. What is the maximum value of g?
- A. 3
- B. 6
- C. −2
- D. 8 ✓
Correct answer: D. Written in vertex form with a negative leading coefficient, the parabola opens downward, so its maximum value is the k-value, 8, which occurs at x = 3.
A sample of a radioactive isotope has a mass, in grams, modeled by A(t) = 800(0.5)^(t/12), where t is the number of days since the sample was measured. To the nearest gram, what is the mass of the sample after 24 days?
- A. 200 ✓
- B. 600
- C. 0
- D. 400
Correct answer: A. After 24 days, t/12 = 2, so A(24) = 800(0.5)² = 800(0.25) = 200 grams.
The function f(x) = 200(0.85)^x models the mass, in grams, of a decaying sample after x years. To the nearest whole percent, by what percent does the mass decrease every 2 years?
- A. 28% ✓
- B. 15%
- C. 30%
- D. 72%
Correct answer: A. Correct — over 2 years the decay factor is (0.85)² = 0.7225, which corresponds to a decrease of about 1 − 0.7225 = 0.2775, or approximately 28%.
The graph of f(x) = −2(x − 3)² + 18 crosses the x-axis at two points. What is the positive difference between the x-coordinates of those two points?
- A. 3
- B. 6 ✓
- C. 9
- D. 18
Correct answer: B. Correct — setting f(x) = 0 gives (x − 3)² = 9, so x − 3 = ±3, meaning x = 0 or x = 6; the positive difference between these zeros is 6.