A rental company purchases a truck for $14,500. The truck requires an average cost of $6.75 per day in maintenance.

(a) Find a linear function that expresses the total cost C of owning the truck after t days.
C(t) =

(b) The truck rents for $55.00 a day. Find a linear function that expresses the revenue R when the truck has been rented for t days.
R(t) =

(c) The profit after t days, P(t), is given by the function P(t) = R(t) − C(t). Find the linear function P(t).
P(t) =

(d) Use the function P(t) that you obtained in part (c) to determine how many days it will take the company to break even on the purchase of the truck. Assume that the truck is in use every day.

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loser

(a) To find the total cost C of owning the truck after t days, we need to consider the initial purchase cost of the truck and the daily maintenance cost. The initial cost is given as $14,500 and the daily maintenance cost is $6.75 per day. So, the linear function that expresses the total cost C(t) after t days can be written as:

C(t) = 14,500 + (6.75 * t)

(b) The revenue R when the truck has been rented for t days is given as $55.00 per day. So, the linear function that expresses the revenue R(t) can be written as:

R(t) = 55.00 * t

(c) The profit after t days, P(t), is given by subtracting the total cost C(t) from the revenue R(t). So, the linear function P(t) can be written as:

P(t) = R(t) - C(t)
= (55.00 * t) - (14,500 + (6.75 * t))
= 48.25 * t - 14,500

(d) To determine how many days it will take the company to break even on the purchase of the truck, we need to find the value of t when the profit (P(t)) is equal to zero.
So, we can set the P(t) function to zero and solve for t:

0 = 48.25 * t - 14,500

Rearranging the equation:

48.25 * t = 14,500

Dividing both sides by 48.25:

t = 14,500 / 48.25

Evaluating the division:

t ≈ 300.51

So, it will take approximately 301 days for the company to break even on the purchase of the truck when it is in use every day.