Create and solve one-variable equations and inequalities from contexts using all studied expression types, including simple root functions.
Write and solve an exponential equation from a context
Problem
An amount starts at \(500\) and grows \(8\%~\text{per}~\text{period}\). Write an exponential equation for reaching \(1000\) and solve for the time \(t\).
Big Picture
What this problem is really about
A repeated percent increase becomes a multiplier greater than one, not the percent written as a decimal by itself. After setting the growth expression equal to the target, divide out the starting amount so only the exponential factor remains. Logarithms then bring the time exponent down where it can be isolated and interpreted in periods.
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