Exponential Relations

Question

A) There is am estimated 2000 deer currently in China. The population is estimated to decrease by 8% every year due to the construction of homes in the area. At this rate how many deer will there be by the year 2030?

B) How would this result change if the deer population was decreasing by 8% every 3 years?

Answer 1

Essentially, this problem asks for the future value of a current number, except that the rate will be a negative number.

 

Part 1.

So, the formula becomes FV= Present x (1-r)^t where r = rate, and t = time

 

Inserting the values, we get FV = 2000 x (1-.08)¹⁴

solving, we get ≅ 622 deer

 

Part 2.

Assuming only a decline, then the rate will be 0.08/3 per year = 0.0266 per year.

So, in 14 years, the population would be ≅ 1370 deer