Help me find this piecewise problem

Question

Write a piecewise equation that models the trucking company model as described below. Let x represent the number of miles traveld and C(x) ) represent the cost for those x miles. The first 100 miles are included in the $ 10.00 transport fee. Each additional mile costs $0.15. Now use your piecewise equation to compute the total transport cost for a customer .

Answer 1

Hi Hajir!

For this piece-wise function, we know that x will represent the number of miles traveled. We also know that for the first 100 miles, the cost, which is C(x), will always be $ 10.00. Therefore, in between when x=0 and x=100, C(x) = $10.00. (This will look like a horizontal line on the graph)

From x=100 onward, C(x) increases by $0.15 for each mile traveled. So we can model that like this:

C(x) = 0.15x + 10.00 <- We have to add 10.00 because that is the base cost no matter how far you go.

Now we just have to put these two components together into a piece-wise function:

C(x) = ⌈ 10.00, 0 < x ≤ 100

⌊ 0.15x + 10.00, x ≥ 100

In order to compute the total cost for your customer, you must first find out how many miles they traveled. If they traveled between 0 and 100 miles, then the cost will be $10.00. If they traveled further than 100 miles, then you need to plug in their mileage into the second equation, where x = miles traveled.

I hope this helped! If you have any questions feel free to reply :)

-Christian A.

Answer 2

The first 10 miles are a flat rate so the first part is C(x)=10 0≤x≤100. The second part has a slope that's not 0 but $0.15 though it is starting from the 10 mark. That makes the piece after C(x)=0.15x+10 x>100.