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Math Help - Exponential Function

  1. #1
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    Exponential Function

    Crescent City, California, has historically been at risk for tsunami waves. The probability P (as a decimal) of no tsunami wave of height 15 feet or more striking Crescent City over a period of Y years decreases as the time interval increases. Increasing the time interval by 1 year decreases the probability by about 2%

    (a) Explain why P is an exponential function of Y.

    For each change in Y of 1 year, the probability P decreases by 2%, , so P exhibits a constant percent change.

    (b) What is the decay factor for P?

    ____per yr

    (I thought this would be 0.02)

    (c) Recall that the probability of a certainty is 1. What is the initial value of P?

    P(0) = 1

    (d) Find a formula for P as a function of Y.

    P = 1(0.02^Y)

    (That has to be wrong.)

    (e) Find a formula for the probability Q that at least one wave 15 feet or higher will strike Crescent City over a period of Y years. (Suggestion: It should be helpful to note that the probability of the occurrence of an event plus the probability that it will not occur is the probability of a certainty, 1.)

    Q =

    (Where the heck did Q come from?)
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  2. #2
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    Quote Originally Posted by MathBane View Post

    (b) What is the decay factor for P?

    ____per yr

    (I thought this would be 0.02)
    It will be 1-0.02 = 0.98
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