The required function is: [tex]f(t) = -0.05t+12[/tex]
Step-by-step explanation:
We have to write a function for the remaining figurines Colin has to paint.
Here
f is the function that represents number of figurines remaining
t represents time in minutes as the unit of measurement is minutes
f will be a function of t
It is mentioned in the problem that after working for 60 minutes, he has 9 figurines left to paint.
This means that
f(60) = 9
It is also given that he takes 20 minutes to paint one figurine which means in 60 minutes he will have painted 3 figurines
So at start total figurines that needed to be painted will be:
9+3 = 12
Which means that
f(0) = 12
By using these two points we can find the slope of the function
[tex]m = \frac{Change\ in\ figurines}{Change\ in\ time}\\m = \frac{9-12}{60-0}\\m = \frac{-3}{60}\\m = -0.05[/tex]
The function will be:
[tex]f(t) = mt+b[/tex]
Putting the value of slope
[tex]f(t) = -0.05t+b[/tex]
b is the initial value of figurines so
[tex]f(t) = -0.05t+12[/tex]
Keywords: Functions, slope
Learn more about functions at:
#LearnwithBrainly
