Question

After 4 days, a bookstore has 140 copies of a new title still on hand. After 9 days, the bookstore has 50 copies still on hand. Model this situation by writing an equation of the form c(t)=mt+b where c is the number of copies still on hand after t days of being available

Answer 1

`c(t) =-18t +212`

Explanation:

Given

`(t_1,c_1) = (4,140)`

`(t_2,c_2) = (9,50)`

Required

Determine the equation

First, we calculate the slope (m)

`m = (c_2 - c_1)/(t_2 - t_1)`

`m = (50 - 140)/(9-4)`

`m = (-90)/(5)`

`m = -18`

The equation is then calculated as:

`c =m(t - t_1) + c_1`

`c =-18*(t - 4) + 140`

`c =-18t +72 + 140`

`c =-18t +212`

Hence, the function is:

`c(t) =-18t +212`