Colin is painting figurines. He spends 20 minutes painting each figurine. After painting for 60 minutes, he still has 9 more figurines left to paint.
The number f of figurines left to paint is a function of t, the amount of time in minutes Colin spends painting.
Answers
Answer:
Answer:
f(t) = -0.05t +12f(t)=−0.05t+12
Step-by-step explanation:
To solve this problem we must pay attention to the following data supplied:
- f It is the number of figurines that remain to be painted.
- t amount of time, in minutes, that Colin spends painting
- Colin takes 20 minutes painting each figurines.
- After painting 60 min, he still has 9 figurines left. f (60) = 9
If he takes 20 minutes painting 1, it means that in 60 minutes he has painted 3 and he has 9 left.
Then, at the beginning he has 9 +3 figurines to be painted.
\begin{gathered}f (0) = 3 + 9\\f (0) = 12\end{gathered}
f(0)=3+9
f(0)=12
With these two points we can find the function:
If m is the slope of the line, then:
\begin{gathered}m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{9-12}{60-0}\\\\m = -0.05\\\\f (t) = -0.05t + c\end{gathered}
m=
x
2
−x
1
y
2
−y
1
m=
60−0
9−12
m=−0.05
f(t)=−0.05t+c
Where by definition c = f(0) = 12c=f(0)=12
Finally the formula is:
f(t) = -0.05t +12f(t)=−0.05t+12
Answer:
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