Question

A company rents moving vans for a charge of $30 plus $0.50 per mile. the company only allows its vans to be user for "in-town" moves, with total mileage limited to 100 miles. the total rental cost, C(m), (in dollars) is a function of the distance m (in miles) that the van is driven. state a rule for the function, graph the function, and state its domain and range

Answer 1

Remember the cost cannot be a number lesser than zero. so the domain must be such that the total cost C(m) is not negative. Also the range will always be 0.5 and above provided our domain is greater than or equal to zero.

Answer 2

Answer:

The function would be:

$C(m)=30+0.50m$

Because the rent cost $30 initially, and then $0.50 per mile additionally. So, the $30 is a constant, and the $0.50 is variable, so it has to be with the independent variable.

However, we need to set one restriction, because the problem says that the total mileage is limited to 100 miles. This means that  $m$ cannot be more than 100 miles, or it could be equal or less than 100 miles.

So, this restriction would be:

$m\leq 100$

Also, if miles are restricted, then, costs are also restricted to less than 100 miles:

$C(m)=30+0.50(100)=80$

Therefore, the cost is not higher than $80:

$C\leq 80$

Therefore, the function and restrictions would be:

$C(m)=30+0.50m$

$m\leq 100$

$C\leq 80$