Question

For each year, t, the population of a forest of trees, call it Forest A, is represented by the function A(t) = 105 (1.025)^t. In a neighboring forest, call it Forest B, the population of the same type of tree is represented by the function B(t) = 87 (1.029)^t.

a. Which forest's population is growing at a faster rate?
b. Which forest had a greater number of trees initially? select an answer By how many (round to the nearest tree)? trees
c. Assuming the population growth models continue to represent the growth of the forests, which forest wil have a greater number of trees after 50 years (round to the nearest tree)?
By how many? _______ trees

Answer 1

Forest B, starting with a lower initial population than Forest A, boasts a greater yearly growth rate that ultimately leads to it having a higher population than Forest A after 50 years.

Step-by-step explanation:

Let's compare the population growth of both forests. Forest A starts with a higher initial population (105 trees) than Forest B (87 trees). However, Forest B is growing at a faster yearly rate (2.9%) than Forest A (2.5%). Therefore, over time, the population of Forest B will increase more rapidly.

To determine which forest will have a greater number of trees after 50 years, we can substitute t=50 in both functions. A(50) = 105(1.025)^50 and B(50) = 87(1.029)^50. Calculating these values, we find that Forest B will have a greater number of trees after 50 years. The exact number by which Forest B exceeds Forest A can be found by subtracting A(50) from B(50).

This calculation illustrates how an initially smaller population (Forest B) can overtake a larger population (Forest A) over time due to a higher growth rate.

Learn more about Exponential Growth