Question

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 fff of figurines left to paint is a function of ttt, the amount of time in minutes Colin spends painting.

Answer 1

f=-1/20t+12

Explanation:

khan

Answer 2

`f(t) =-(1)/(20) t + 12`

Explanation:

Given

`t \to time`

`f \to figurines`

Required

Determine the function

From the question, we have:

`60\ minutes \to 9\ left`

This is represented as:

`f(60) = 9` or
`(60,9)`

If he spends 20 minutes on 1 figurine;

`20\ minutes = 1\ figurine`

Multiply both sides by 3

`60\ minutes = 3\ figurines`

This means that, he spends 60 minutes on 3

plus he still has 9 left

So, the initial figurines is:

`f(0) =3 + 9`

`f(0) =12` or
`(0,12)`

So, we have:

`(60,9)` and
`(0,12)`

Calculate the slope (m)

`m = (y_2 -y_1)/(x_2 - x_1)`

`m = (12- 9)/(0 -60)`

`m = (3)/( -60)`

`m = -(1)/(20)`

The equation is then calculated as;

`f(t) = m * t + c`

`f(t) = -(1)/(20) * t + c`

`f(t) = -(1)/(20)t + c`

To solve for c, we have:

`f(60) = 9`

So, we have:

`9 = -(1)/(20) * 60 + c`

`9 = -3 + c`

Add 3 toboth sides

`c =12`

Hence, the equation is:

`f(t) =-(1)/(20) t + c`

`f(t) =-(1)/(20) t + 12`