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Homework Help: Exponetial Function

  1. Jul 11, 2006 #1
    A particular company required [tex]P[/tex] tonnes of fossil fuel in 1990. Figures suggest that this annual requirement is increasing in such a way that [tex]t[/tex] years after 1990 the company will require [tex]Pe^0.1t[/tex] 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,
  2. jcsd
  3. Jul 11, 2006 #2
    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!
  4. Jul 11, 2006 #3
    thanks mate, that helps a lot :smile:
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