create an equation (use "t" for years) that would show how many moths are in the forest for any year

Question

increase every year by 8%

in 1975 there were 4,534 moths

Answer 1

Let's say number of moths = M.

 

In 1975, M = 4534.

Let's set 1975 at t = 0 (year 0).

 

And what you know is that M increases by 8% (0.08) every year (t). So, it goes up by a factor of 1.08.

 

Now let's put all this together in an equation:

M = 4534 (1.08)^t

 

Why do you raise 1.08 to the t power? Because t represents every additional year that the 8% increase occurs, and you multiply that by your starting M in t = 0, since the number of moths increases depending on the amount of moths already there, and it keeps compounding on what is the new number.