Question

A scientist is studying wildlife. she estimates the population of bats in her state to be 270,000. she predicts the population to grow at an average annual rate of 2.9%. using the scientist's prediction, create an equation that models the population of bats, y, after x years.

Answer 1

Growth rate = 2.9% = 0.029

After 1 year,    y = 270000*(1 +0.029) = 270000*1.029
After 2 years, y = (270000*1.029)*1.029 = 270000*(1.029^2)

After x years, the population is
y = 270000*(1.029^x)

Answer: $y =270000( 1.029^{x} )$