Create equations in two or more variables and graph them with appropriate labels and scales.
Write a two-variable exponential equation from an initial value and a percent change
Problem
Write a \(\text{two}\text{-}\text{variable}\) exponential equation for population \(P\) that starts at \(500\) and grows by \(6\%~\text{each}~\text{year}\), where \(t\) is years.
Big Picture
What this problem is really about
A fixed percent increase each year means the population is multiplied by the same growth factor repeatedly. We’ll convert the percent to a decimal, add it to one to keep the original amount plus the growth, and use initial population times that factor to the number of years.
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