Chapter 2.4, Problem 25E

(a)

To determine

The percentage of extremely wealthy households used the internet according to the given model. The following graph shows the percentage of U.S. households using the internet at home in $2010$ as a function of household income.

The logistic model is,

$P\left(x\right)=\frac{95.0}{1+2.78{\left(1.064\right)}^{-x}}\text{percent}$

Where $x$ is household income in thousands of dollars.

(b)

To determine

To calculate: The exponential model that best approximates $P\left(x\right)$ for small $x$. The logistic model is,

$P\left(x\right)=\frac{95.0}{1+2.78{\left(1.064\right)}^{-x}}\text{percent}$

Where $x$ is household income in thousands of dollars.

(c)

To determine

To calculate: The income household whose $50\%$ percentage used for the internet in $2010$ according to the given model.

The logistic model is,

$P\left(x\right)=\frac{95.0}{1+2.78{\left(1.064\right)}^{-x}}\text{percent}$

Where $x$ is household income in thousands of dollars.