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Answer:
[tex]f(t) =-\frac{1}{20} t + 12[/tex]
Step-by-step explanation:
Given
[tex]t \to time[/tex]
[tex]f \to figurines[/tex]
Required
Determine the function
From the question, we have:
[tex]60\ minutes \to 9\ left[/tex]
This is represented as:
[tex]f(60) = 9[/tex] or [tex](60,9)[/tex]
If he spends 20 minutes on 1 figurine;
[tex]20\ minutes = 1\ figurine[/tex]
Multiply both sides by 3
[tex]60\ minutes = 3\ figurines[/tex]
This means that, he spends 60 minutes on 3
plus he still has 9 left
So, the initial figurines is:
[tex]f(0) =3 + 9[/tex]
[tex]f(0) =12[/tex] or [tex](0,12)[/tex]
So, we have:
[tex](60,9)[/tex] and [tex](0,12)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{12- 9}{0 -60}[/tex]
[tex]m = \frac{3}{ -60}[/tex]
[tex]m = -\frac{1}{20}[/tex]
The equation is then calculated as;
[tex]f(t) = m * t + c[/tex]
[tex]f(t) = -\frac{1}{20} * t + c[/tex]
[tex]f(t) = -\frac{1}{20}t + c[/tex]
To solve for c, we have:
[tex]f(60) = 9[/tex]
So, we have:
[tex]9 = -\frac{1}{20} * 60 + c[/tex]
[tex]9 = -3 + c[/tex]
Add 3 toboth sides
[tex]c =12[/tex]
Hence, the equation is:
[tex]f(t) =-\frac{1}{20} t + c[/tex]
[tex]f(t) =-\frac{1}{20} t + 12[/tex]