Chapter 4.1, Problem 4E

Reminder Round all answers to two decimal places unless otherwise indicated.

Amazon Sales One article states that each one-second delay in loading search results has the effect of multiplying the probability that an online customer will make a purchase by $0.90$. Let $P$ denote the probability, as a perecntage, that an Amazon customer will make a purchase if the search result require $t\text{seconds}$ to load. Suppose that at the time a customer initiates a search for flatware, the probability that she will make a purchase is $50\%$.

a. Make an exponential model that shows the probability $P$ as a function of $t$.

b. What is the probability of a sale if it takes $5\text{seconds}$ to load search results?

c. Plot the graph of $P$ versus $t$ over a $1\text{-minute}$ period.