Chapter 2.4, Problem 26E

Internet Use The following graph shows the percentage of U.S. residents who used the Internet at home in 2010 as a function of income (the data points) and a logistic model of these data (the curve).⁵⁰

The logistic model is given by

$P\left(x\right)=\frac{86.2}{1+2.49{\left(1.054\right)}^{-x}}$ percent where x is the household income in thousands of dollars.

a. According to the model, what percentage of extremely wealthy people used the Internet at home?

b. For low incomes the logistic model is approximately exponential. Which exponential model best approximates $P\left(x\right)$ forsmall x?

c. According to the model, 50% of individuals with what household income used the Internet at home in 2010? (Round the answer to the nearest $1,000.)