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?
(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.)
(Where the heck did Q come from?)