Question

The amount of CO2 emitted per year A (in tons) for a vehicle that averages x miles per gallon of gas, can

be approximated by the function A(x) = 0.0089x2 – 0.815x + 22.3.
a) Determine the average rate of change of the amount of CO2 emitted in a year over the interval
[20, 25), and interpret its meaning.

Answer 1

Average Rate of Change = -0.4145

It means that the amount of CO2 emitted per year will decrease by an averaage rate of 0.4145 (tons - gallon of gas)/mile

Explanation:

In order to solve this problem, we can make use of the Average Rate of Change formula, which looks like this:

`ARC=(A(25)-A(20))/(25-20)`

So we need to start by finding what A(25) is equal to, so we get:

`A(25)= 0.0089(25)^(2)-0.0815(25)+22.3`

so

A(25)=7.4875

next, we can find A(20)

`A(20)=0.0089(20)^(2)-0.0815(20)+22.3`

so we get:

A(20)=9.56

so now we can use the average rate of change formula:

`ARC=(A(25)-A(20))/(25-20)`

`ARC=(7.4875-9.56)/(25-20)`

ARC=-0.4145

and It means that the amount of CO2 emitted per year will decrease by an averaage rate of 0.4145 (tons - gallon of gas)/mile