Question

3 days after picking apples, a family had 100 apples left. After 6 days, 76 apples were left. Assuming a linear function, write an equation in the form a(t)=mt+b that shows the number of apples, a(t), left t days after picking them. Be sure to include "a(t) =" in your answer.

Answer 1

a(t) = -8t + 124

Explanation:

The number of apples left 3 days after picking them is given by the following equation:

`a(t) = mt + b`

3 days after picking apples, a family had 100 apples left.

This means that
`a(3) = 100`

So

`100 = 3m + b`

`3m + b = 100`

`b = 100 - 3m`

After 6 days, 76 apples were left.

So a(6) = 76. Then

`76 = 6m + b`

Since b = 100 - 3m

`76 = 6m + 100 - 3m`

`3m = -24`

`m = (-24)/(3)`

`m = -8`

b:

`b = 100 - 3m = 100 - 3*(-8) = 124`

So

a(t) = -8t + 124.