SAT Nonlinear functions Practice Question 16 (Hard)

Math · Advanced MathHard

The function $m(t) = 80\left(\frac{1}{2}\right)^{\frac{t}{6}}$ gives the mass, in grams, of a radioactive sample $t$ days after it was measured. Which function gives the mass, in grams, of the sample $w$ weeks after it was measured?

$80\left(\frac{1}{2}\right)^{\frac{6w}{7}}$

$80\left(\frac{1}{2}\right)^{\frac{w}{42}}$

$80\left(\frac{1}{2}\right)^{\frac{7w}{6}}$

$80\left(\frac{1}{2}\right)^{42w}$

Show answer and explanation

Answer: C

There are 7 days in a week, so $w$ weeks equals $t = 7w$ days. Substitute: $m = 80\left(\frac{1}{2}\right)^{\frac{7w}{6}}$ .

Choice A converts in the wrong direction, dividing by 7 instead of multiplying.

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