Question

Each year, a group of 150 Alaskan wolves has an average birth rate of 15% and an average death rate of 37% per year. Which function could be used to predict when there will be 25 wolves in this group?
A. 150( (1.15)^t - (0.63)^t ) = 25
B. 150( (1.15)^t - (0.37)^t ) = 25
C. 150 (1.15 - 0.63)^t =25
D. 150 (1.15 - 0.37)^t =25

Answer 1

Given that the starting population is 150 wolves, let the time when there will 25 wolves left be x, then
The increase in the number of wolves due to births is given by 150(1 + 0.15)^t = 150(1.15)^t
The decrease in the number of wolves due to dirths is given by 150(1 - 0.37)^t = 150(0.63)^t.
The number of wolves at time t is given by 150(1.15)^t - 150(0.63)^t = 150((1.15)^t - (0.63)^t).

Therefore, the function that could be used to predict when there will be 25 wolves in this group  is 150((1.15)^t - (0.63)^t) = 25. (option A).