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

Answer:

a(t) = -8t + 124

Step-by-step 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

$76 = 6m + 100 - 3m$

$3m = -24$

$m = \frac{-24}{3}$

$m = -8$

b:

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

So

a(t) = -8t + 124.