Question

The cost​ C, in​ dollars, of renting a moving truck for a day is given by the function C(x)=0.20x+45, where x is the number of miles driven.
(a) What is the cost if a person drives x=160 ​miles?
​(b) If the cost of renting the moving truck is ​$120​, how many miles did the person​ drive?
​(c) Suppose that a person wants the cost to be no more than ​$200. What is the maximum number of miles the person can​ drive?
(d) What is the implied domain of​ C?
(e) Interpret the slope.
(f) Interpret the​ y-intercept.

Answer 1

Answer:

(a) The cost if a person drives 160 miles is 77 dollars

(b) the person drive 375 miles

(c) the maximum number of miles the person can drive is 775 milles

(d) the implied domain of C is numbers bigger than zero

(e) the slope says how cost every mille that a person drive .

(f) the y- intercept says what is the minimum value of renting the truck even if a person doesn’t drive any mile.

Step-by-step explanation:

The Cost C is given by the function: C(x)=0.2*x+45

Then, for calculate the cost if a person drives 160 miles, we should replace x by 160 miles in the function, So:

C(x)=0.2*160+45

C(x)=77 dollars

For calculate how many miles did the person drive if the cost of renting is 120, we replace C(X) with 120 and solve for x as:

120=0.2*x+45

120-45=0.2*x

X=375 miles

For calculate  the maximum number of miles the person can drive if that person wants the cost to be no more than $200, we replace C(X) with 200 and solve for x as:

200=0.2*x+45

200-45=0.2*x

X=775 miles

In this case, we know that the cost could be 200 or less then if the person drive 775 miles or less, the cost is always going to be less than 200.

The domain are the values that the variable x can take, so it make sense that a person can drive any value of miles that are bigger than zero.

The slope of the function is the number that is multiplied with the variable x, so this number say what is the cost of every mile that a person drive. This means that every mile driven cost 0.2 dollars

The y intercept is the value that doesn’t have a variable multiplying. this is the fixed cost of renting a car, so if a person drive zero miles the cost of renting is 45 dollars.