# Math Help - exponent application question help

1. ## exponent application question help

A substance increases by 25% every 5 minutes. If the current population of substance is 400, how long will it take the population to reach 1 million?

2. ## Re: exponent application question help

The basic equation that you need to work is this:

$400 \times 1.25^N = 1,000,000$

where N = the number of 5-minute periods. You can manipulate it as follows:

$1.25^N = \frac {1,000,000}{400} = 2500$

$\log (1.25^N) = N \log(1.25) = \log(2500)$

$N = \frac {\log(2500)}{\log 1.25}$

Now you have N, and the time required is 5 minutes times that.

3. ## Re: exponent application question help

"Increases by 25%" means it goes from A to A+ .25A= (1.25)A every 5 minutes. That is, every 5 minutes you multiply by 1.25:
If it starts at 400, in 5 minutes it will be 400(1.25). After 10= 2(5) minutes it will be multiplied by 1.25 again- it will now be $400(1.25)(1.25)= 400(1.25)^2$. After 15= 3(5) minutes it will be multiplied by 1.25 another time- it will now be $400(1.25)(1.25)(1.25)= 400(1.25)^3$. In t minutes there will be N= t/5 periods of 5 minutes and so the 400 will have been multiplied by 1.25 t/5 times giving ebaines' $400(1.25)^N$