Originally Posted by

**22upon7** I am provided with an example for an Exponential mode, but I can't understand parts of it, I'd appreciate if some one could explain them a bit more.

Question:

*There are apporximately ***ten times as many red kangaroos as grey kangatoos** **<<<<< see question 2** in a certain area. If the population of grey kangaroos increases at a rate of 11% per annum while that of the red kangaroos decreases at 5% per annum, find how many years must elapse before the proportions are reversed, assuming the same rates continue to apply.

Solution

Let $\displaystyle P$ = population of grey kangaroos at the start.

Therefore the number of grey kangaroos after $\displaystyle n$ years = $\displaystyle P(1.11)^n$

The number of red kangaroos after $\displaystyle n$ years = $\displaystyle 10P(0.95)^n$

**Question 1 : Why is the percentage raised to the power of **$\displaystyle n$** (+n years later)?**

When Proportions are reversed:

$\displaystyle P(1.11)^n = 10* [10P(0.95^n)]$

$\displaystyle (1.11)^n = 100(0.95)^n$

**Question 2 : Why is $\displaystyle [10P(0.95^n)]$ multiplied by **$\displaystyle 10$**? **