The rate of change (in thousands of people per year) of the population of a town between 2000 and 2012 can be modeled by
$$R(t) = 1.5e^{0.03t},$$
where $t$ is the number of years after 2000. Assume the population continues to grow in this manner. How many years from now (2012) will it take for the population to increase by 25,000 people?
- I'm a bit confused for this one because I know that to find an amount you use the derivative of the equation.
- I took the derivative of $R(t)$ and set it equal to 25,000 so my new equation looks like this: $25,000=(0.03)(1.5)e^{0.03t}$
- This gave me a huge answer around 440 years so I'm just not sure what I'm doing wrong.