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
The function of the number of hours (t) that it took Anumeha to complete the work is f = 5t + 10.
A linear function has one independent variable(x) and one dependent variable(y) and it can be represented as:
y =f(x) = mx + b
where;
From the given information, the function illustrating the fee of Anumeha shows that it is a linear function.
Thus, we can say function's formula is expressed as;
f = mt + b
where;
However, the y-intercept relates to the (f) value when t = 0, which implies that this relates to the initial fee prior to Anumeha starting any work.
Thus, when:
f = mt + 10
35 = 5m + 10
35 - 10 = 5m
5m = 25
m = 25/5
m = 5
Therefore, we can conclude that the linear function formula of the number of hours (t) that it took Anumeha to complete the work is f = 5t + 10.
Learn more about linear functions here:
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