Chapter 1, Problem 1CE

To determine

An expression for the cost to buy and run the hot water tank for x years.

Answer to Problem 1CE

Solution:

The expression is obtained as:

$\underset{\_}{\text{C}\left(x\right)=\text{\$}218+508x}$

Explanation of Solution

Given:

Retail cost of 40-gallon electric hot water is equal to $\$218$ and the estimated annual cost of operation $\$508$.

Explanation:

The cost function can be estimated as:

$\text{C}\left(\text{x}\right)\text{=mx+b}$

Where,

The term m is the annual cost.

The term b is the fixed cost or the initial cost.

The term x is the number of years.

With an initial cost of $\$218$ and an annual cost of $\$508$, for x years of operation, the cost C for 40-gallon electric hot water is:

$C\left(x\right)=218+508\left(x\right)$

Hence, the expression is obtained as:

$\underset{\_}{\text{C}\left(x\right)=\text{\$}218+508x}$