Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Write and solve an exponential equation from a repeated-factor context
Problem
A population has \(100~\text{organisms}\) at time \(t=0~\text{hours}\) and doubles each hour. Write and solve an exponential equation for the elapsed time when the population reaches \(800~\text{organisms}\).
Big Picture
What this problem is really about
Doubling each hour is repeated multiplication, so the elapsed time belongs in the exponent of an exponential model. We’ll set initial amount times the doubling factor to the time power equal to the target, divide out the initial amount, and identify how many factors of two produce the remaining ratio.
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