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.

Question

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Respuesta :

ajdonis ajdonis · Answer 1 · 2020-12-15T01:24:31+01:00

Answer:

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

Step-by-step explanation:

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

[tex]ARC=\frac{A(25)-A(20)}{25-20}[/tex]

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

[tex]A(25)= 0.0089(25)^{2}-0.0815(25)+22.3[/tex]

so

A(25)=7.4875

next, we can find A(20)

[tex]A(20)=0.0089(20)^{2}-0.0815(20)+22.3[/tex]

so we get:

A(20)=9.56

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

[tex]ARC=\frac{A(25)-A(20)}{25-20}[/tex]

[tex]ARC=\frac{7.4875-9.56}{25-20}[/tex]

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