Calculating Exponential Function Increase for Fossil Fuel Use 1990-2010

[pavadrin]

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?

thanks in advance,
Pavadrin

 

[DLinkage]

yes you can put in any value of p it doesn't 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!

 

[pavadrin]

thanks mate, that helps a lot