Thread: Exponential Models and Application help

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 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 = population of grey kangaroos at the start.

Therefore the number of grey kangaroos after years =

The number of red kangaroos after years =

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

When Proportions are reversed:




Question 2 : Why is multiplied by ?

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 = population of grey kangaroos at the start.

Therefore the number of grey kangaroos after years =

The number of red kangaroos after years =

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

When Proportions are reversed:




Question 2 : Why is multiplied by ?

I'll take the 2nd line of your calculation:



Use logarithms to determine n:

Thanks, I understand the final Log part of the question.

What I don't understand is why the percentage is raised to the power of n/number of years?

Also doesn't the equation for red kangaroos [10P(0.95^n)] already reflect the fact that it is 10 times more than the number of Grey Kangaroos?

Thanks again,

Dru

Originally Posted by 22upon7

Thanks, I understand the final Log part of the question.

What I don't understand is why the percentage is raised to the power of n/number of years?

Also doesn't the equation for red kangaroos [10P(0.95^n)] already reflect the fact that it is 10 times more than the number of Grey Kangaroos? <<<<< Yes

Thanks again,

Dru

Let's start at the beginning:

At the beginning you have a population of P animals and the population increases by 11% per year:






....