MATH HELP ( growth models)

Question

Suppose the population of a small town is 11000 and growing exponentially at 1.8 %. How many years until the population reaches 26000?

Answer 1

The problem is an exponential growth problem. The equation is Population = 11,000 times e^{0.018 x years}

Our target is 26000. 26000/11000 = e^{0.018 x years} This simplifies to 26/11 = e^{0.018 x years} .

Take the natural log of both sides gives 3.2581 - 2.3979 = 0.018 x years.

Simplifies to 0.8692 = 0.018 x years. Divide both sides by 0.018 gives 47.79 or 48 years.