The table shows four values of x and their corresponding... | SAT Nonlinear functions Question, Answer Explained

Math · Advanced MathMedium

$x$	$f(x)$
0	640
1	480
2	360
3	270

The table shows four values of $x$ and their corresponding values of $f(x)$ for the function $f$ . Which equation could define $f$ ?

$f(x) = 640 - 160x$

$f(x) = 640(0.25)^x$

$f(x) = 640(0.75)^x$

$f(x) = 480(0.75)^x$

Show answer and explanation

Answer: C

Each value of $f(x)$ is $0.75$ times the one before it: $\frac{480}{640} = \frac{360}{480} = \frac{270}{360} = 0.75$ . So $f$ is exponential with base $0.75$ , and $f(0) = 640$ is the starting value. Thus $f(x) = 640(0.75)^x$ .

Choice A fits the first two rows, but it gives $f(2) = 320$ , not $360$ .

Why the other choices are wrong

A. This fits the first two rows, but it gives f(2) = 320, not 360. The values drop by different amounts each time.
B. 0.25 is the fraction lost each step, not the fraction kept. Each value is 0.75 times the one before.
D. 480 is f(1). The starting value, f(0), is 640.

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