Question

Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus $6 for each hour of work. Her total fee for a 4-hour job, for instance, is $32.

Let F(t) denote Carolina's fee for a single job F (measured in dollars) as a function of the number of hours "t" it took her to complete it.
Write the function's formula.

Answer 1

6*4 = 24

32-24 = 8

so her initial fee is $8

so function is:

F(t) = 8 + 6(t)

Answer 2

f(t) = 6 t+8

Explanation:

For every mowing job, she charges an initial fee plus $6 for each hour of work. Constant rate is $6 for every hour

WE use linear equation f(t) = mt + b

Here m is the constant rate = 6

Her total fee for a 4-hour job, for instance, is $32.

That means f(t) is 32 when t= 4

Now we plug in the values and find out b, m=6

f(t) = mt + b

32 = 6(4) + b

32= 24 + b

Subtract 24 on both sides

8 = b

Function f(t) = mt + b

Plug in m=6 and b =8

So function formula becomes f(t) = 6 t+8