Tsunami waves in Crescent City: Crescent City, California, has historically been at risk for tsunami waves.4 The probability P (as a decimal) of no tsunami wave of height 15 feet or more striking...

Tsunami waves in Crescent City: Crescent City, California, has historically been at risk for tsunami waves.4 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 probability5 by about 2%.

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

b. What is the decay factor for P?

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

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

e. What is the probability of no tsunami waves 15 feet or higher striking Crescent City over a 10- year period? Over a 100-year period?

f. 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.)