SAT question 9afe2370 (Nonlinear Functions)

Question

The population P of a certain city y years after the last census is modeled by the equation below, where r is a constant and P0 is the population when y = 0 . P = P0 (1 + r)^y If during this time the population of the city decreases by a fixed percent each year, which of the following must be true?

College Board · Accepted Answer

The correct answer is B. Choice B is correct. The term (1 + r) represents a percent change. Since the population is decreasing, the percent change must be between 0% and 100% . When the percent change is expressed as a decimal rather than as a percent, the percentage change must be between 0 and 1 . Because (1 + r) represents percent change, this can be expressed as 0 < 1 + r < 1 . Subtracting 1 from all three terms of this compound inequality results in -1 < r < 0 .

CookSAT · Answer

Note: The ratio f(1)/f(0) equals 1+r. Testing a list of r values shows the ratio is between 0 and 1 only when r is between -1 and 0.

Explanation

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Why the other choices are wrong

SAT Question 9afe2370: Nonlinear Functions answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong