SAT Nonlinear functions Practice Question 10 (Medium)

Math · Advanced MathMedium

$x$	$f(x)$
0	3
1	12
2	48

The table shows three values of $x$ and their corresponding values of $f(x)$ for the exponential function $f$ . Which equation defines $f$ ?

$f(x) = 9x + 3$

$f(x) = 4(3)^x$

$f(x) = 12x^2$

$f(x) = 3(4)^x$

Show answer and explanation

Answer: D

For an exponential function $f(x) = a(b)^x$ , $f(0) = a = 3$ . Each time $x$ increases by 1, $f(x)$ is multiplied by $\frac{12}{3} = 4$ , and $\frac{48}{12} = 4$ confirms it. So $f(x) = 3(4)^x$ .

Choice A fits the first two rows but gives $f(2) = 21$ , not 48.

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