Anumeha is mowing lawns for a summer job. for every mowing job, she charges an initial fee of \$10$10dollar sign, 10 plus a constant fee for each hour of work. her fee for a 555-hour job, for instance, is \$35$35dollar sign, 35. let f(t)f(t)f, left parenthesis, t, right parenthesis denote anumeha's fee for a single job fff (measured in dollars) as a function of the number of hours ttt it took her to complete it. write the function's formula.

Since the problem specifically states that the fee of Anumeha is constant for the each hour of work with an initial fee of $10, therefore this means that the function must be linear. The general form of a linear function is in the form of:

y = m x + b

In this case, y = f and x = t, therefore:

f = m t + b

where f is a single job, m is the slope of the linear function, t is number of hours and b is the y intercept

The y intercept (b) is the value of f when t = 0, in this case this is equivalent to the initial fee (before any work is done) therefore:

b = 10

Thus the equation becomes:

f = m t + 10

We are also given that for t = 5, the total fee is $35 so f = 35. Therefore calculating for m:

35 = m (5) + 10

5m = 25

m = 5

Thus,

f = 5 t + 10

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