Exponential Functions · Exercise 22

Consider this scenario: For each year $t,$ the population of a forest of trees is represented by the function $A\left(t\right)=115{\left(1.025\right)}^t.$ In a neighboring forest, the population of the same type of tree is represented by the function $B\left(t\right)=82{\left(1.029\right)}^t.$ (Round answers to the nearest whole number.)

Discuss the above results from the previous four exercises. Assuming the population growth models continue to represent the growth of the forests, which forest will have the greater number of trees in the long run? Why? What are some factors that might influence the long-term validity of the exponential growth model?

This is an open-ended exercise: its source gives no single answer.

OpenStax, Algebra and Trigonometry 2e · §6.1 Exponential Functions · Exercise 22