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

Answer:

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

Step-by-step explanation:

Given

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

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

Required

Determine the equation

First, we calculate the slope (m)

$m = \frac{c_2 - c_1}{t_2 - t_1}$

$m = \frac{50 - 140}{9-4}$

$m = \frac{-90}{5}$

$m = -18$

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:

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