Question

How do you know When to use an exponential growth model?

Answer 1

When the growth is at an approximately constant percent per unit time, an exponential model works well.

Explanation:

For example, if a population is growing at 4% per year, with an initial population of 1000, then `P=f(t)=1000*1.04^t` is a good model. Note that `(f(t+1))/f(t)=1.04` for all `t`, meaning that there is 4% growth over every time interval of length 1.

This can also be written in terms of `e approx 2.71828` as `P=f(t)=1000*e^(kt)`. The value of `k` is determined by setting `e^(k)=1.04` so that `k=ln(1.04) approx 0.0392`.

This means that a 4% growth rate per unit time corresponds to approximately 3.92% instantaneous growth rate. This basically means that the tangent line at any point grows by approximately 3.92% over a time interval of length 1.