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

(a) Explain whyPis an exponential function ofY.

For each change inYof 1 year, the probabilityPdecreases by 2%, , soPexhibits a constant percent change.

(b) What is the decay factor forP?

____per yr

(I thought this would be 0.02)

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

P(0) = 1

(d) Find a formula forPas a function ofY.

P= 1(0.02^Y)

(That has to be wrong.)

(e) Find a formula for the probabilityQthat at least one wave 15 feet or higher will strike Crescent City over a period ofYyears. (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?)