SAT Nonlinear functions Practice Question 2 (Easy)

Math · Advanced MathEasy

A colony of bacteria has $500$ bacteria at time $t = 0$ , and the number of bacteria doubles every hour. Which function gives the number of bacteria, $P(t)$ , after $t$ hours?

$P(t) = 500(2)^t$

$P(t) = 2(500)^t$

$P(t) = 500 + 2t$

$P(t) = 500t^2$

Show answer and explanation

Answer: A

An exponential model has the form $P(t) = a(b)^t$ , where $a$ is the starting amount and $b$ is the growth factor per unit of time. Here $a = 500$ and doubling means $b = 2$ , so $P(t) = 500(2)^t$ .

Choice B swaps the starting amount and the growth factor.

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