# Exponetial Function

1. Jul 11, 2006

A particular company required $$P$$ tonnes of fossil fuel in 1990. Figures suggest that this annual requirement is increasing in such a way that $$t$$ years after 1990 the company will require $$Pe^0.1t$$ tonnes. By what percentage of the 1990 tonnage will the requirement have increased by the year 2010?

For this problem would i need to substitute a fixed value for P, and then set t to zero (for calculating the amount that was used in 1990) and then change the value to 20 for the year 2010?

2. Jul 11, 2006

yes you can put in any value of p it doesnt matter. I'll show you why, suppose the function was y = P*e^(3t)

when t = 0 we have P
when t = 3 we have Pe^3

The increase is simply Pe^3 - P or P*(e^3 - 1)

The percent increase is the increase divided by the initial value, so if the initial value is P then we have P/P*(e^3 - 1) = (e^3 - 1)

Then of course you need to multiply by 100 if you are putting the answer in terms of percentage.

I think you can figure out the restof your question using this example.
Good Luck!

3. Jul 11, 2006