Question

c

1. the average cost per year in electricity for a widescreen television is approximately $18.

a) assume that a new television costs $1299. determine the total annual cost for a television that lasts for 10 years. (assume the only costs associated with the television are its purchase cost and electricity.)
b) develop a function that gives the annual cost of the television as a function of the number of years that the television is owned.

Explanation:

Step1: Calculate total electricity cost for 10 years

The average cost per year in electricity is $18. For 10 years, the electricity cost is \(18\times10 = 180\) dollars.

Step2: Calculate total annual cost

The purchase cost of the television is $1299. The total cost over 10 years (purchase cost + electricity cost) is \(1299+180=1479\) dollars.

Step3: Develop the function for part (b)

Let \(y\) be the number of years the television is owned. The purchase cost is $1299 (a one - time cost) and the electricity cost per year is $18. The total cost \(C(y)\) is the sum of the average purchase cost per year (\(\frac{1299}{y}\)) and the annual electricity cost (18). So the function is \(C(y)=\frac{1299}{y}+18\)

Answer:

a) The total annual cost for a television that lasts for 10 years is \(\$1479\)
b) The function that gives the annual cost of the television as a function of the number of years \(y\) that the television is owned is \(C(y)=\frac{1299}{y}+18\)