An equipment rental company rents power tools to those in need. The rental fee for every tool is $100 for the first 3 hours and then $50 for each additional hour. This fee can be modeled by the function C(t) = 100 + 50(t - 3), there C represents the total cost and t represents the the time in hours. Complete the statement:

Question

C(7) =
, meaning that the cost for renting a piece of equipment for 7 hours is

What does C(5) = 200 mean in the context of this problem?

Answer 1

To find \( C(7) \), we can use the given cost function:

\[ C(t) = 100 + 50(t - 3) \]

Substituting \( t = 7 \) into the function:

\[ C(7) = 100 + 50(7 - 3) \] \[ = 100 + 50 \times 4 \] \[ = 100 + 200 \] \[ = 300 \]

So, \( C(7) = 300 \), meaning that the cost for renting a piece of equipment for 7 hours is $300.

Now let's interpret \( C(5) = 200 \) in the context of this problem:

Using the function again, substitute \( t = 5 \):

\[ C(5) = 100 + 50(5 - 3) \] \[ = 100 + 50 \times 2 \] \[ = 100 + 100 \] \[ = 200 \]

Thus, \( C(5) = 200 \) means that the cost for renting a piece of equipment for 5 hours is $200.