For each year 𝑡, the population of trees in forest A is represented by the function 𝐴(𝑡)=124(1.22)^𝑡 . In forest B, the population of trees is represented by the function 𝐵(𝑡)=149(1.15)^𝑡 .

Question

Which forest had a greater number of trees initially?

By how many? Round your answer to the nearest whole number

Answer 1

In an exponential function of the form f(t) = A•B^t, the initial value of the function is A. (This is because the initial value is when t = 0, and A•B^t = A•1 = A).

In 𝐴(𝑡)=124(1.22)^𝑡 the initial value is 124.

In 𝐵(𝑡)=149(1.15)^𝑡 the initial value is 149.

149 > 124, so forest B had the greater number of trees initially.

149 - 124 = 25, so forest B initially had 25 more trees than forest A.