the monthly cost of owning and driving a car typically depends on the number of miles driven. isabel found…

the monthly cost of owning and driving a car typically depends on the number of miles driven. isabel found that in may her driving cost was $451 for driving 478 miles. in june, her cost was $674 for driving 1370 miles.\na. what was the difference in mileage driven in the months of may and june?\nmiles\nb. what was the change in cost corresponding to her mileage changing in may and june?\n$\nc. what is the average rate of change in cost as her mileage changes?\nselect an answer \nd. find a function for the cost, c, of driving m miles each month.\nenter your answer using function notation.\nquestion help: message instructor

the monthly cost of owning and driving a car typically depends on the number of miles driven. isabel found that in may her driving cost was $451 for driving 478 miles. in june, her cost was $674 for driving 1370 miles.\na. what was the difference in mileage driven in the months of may and june?\nmiles\nb. what was the change in cost corresponding to her mileage changing in may and june?\n$\nc. what is the average rate of change in cost as her mileage changes?\nselect an answer \nd. find a function for the cost, c, of driving m miles each month.\nenter your answer using function notation.\nquestion help: message instructor

Answer

Explanation:

Step1: Calculate mileage difference

Subtract May - mileage from June - mileage. $1370 - 478=892$

Step2: Calculate cost - change

Subtract May - cost from June - cost. $674 - 451 = 223$

Step3: Calculate average rate of change

The average rate of change is the change in cost divided by the change in mileage. $\frac{223}{892}=0.25$

Step4: Find the cost - function

We know the equation of a line is $C(m)=am + b$, where $a$ is the slope (average rate of change) and we can use one of the points $(m_1,C_1)$ to find $b$. Using the point $(478,451)$ and $a = 0.25$: $451=0.25\times478 + b$ $451 = 119.5+b$ $b=451 - 119.5=331.5$ So the cost - function is $C(m)=0.25m + 331.5$

Answer:

A. 892 B. 223 C. 0.25 D. $C(m)=0.25m + 331.5$