Question

The bear population in canada was 380,000 in the year 2015, and environmentalists think that the population is increasing at a rate of 2.5% per year

Answer 1

The bear population after t years will be:

p(t) = 380,000*(1 + 0.025)^t

Explanation:

Here the question is missing, so i will found an equation that can tell us the bear population as a function of the number of years that have passed since 2015, represented with the variable t.

The initial bear population in Canada was 380,000.

Each year the population increases by a 2.5%

Then after one year, the population is:

p(1) = 380,000 + 380,000*(2.5%/100%)

p(1) = 380,000 + 380,000*(0.025) = 380,000*(1 + 0.025)

After another year the population increases by 2.5% again, then the new population will be:

p(2) = 380,000*(1 + 0.025) + 380,000*(1 + 0.025)*(2.5%/100%)

p(2) = 380,000*(1 + 0.025) + 380,000*(1 + 0.025)*(0.025)

p(2) = 380,000*(1 + 0.025)*(1 + 0.025)

p(2) = 380,000*(1 + 0.025)^2

So we already can see the pattern here, the bear population after t years will be:

p(t) = 380,000*(1 + 0.025)^t