Question

A handbag company had 5% of the market in 2011 in 2015 it had 23%.

(a) Write a linear equation expressing the percentage of the luxury handbag market y that the company had x years after 2000

Answer 1

`y = 0.045x -0.445`

Explanation:

Given

`(x_1,y_1)=(11,5\%)` ---- in 2011

`(x_2,y_2)=(15,23\%)` --- in 2015

Required

Linear equation for x years after 2000

First, calculate the slope

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

`m = (23\% - 5\%)/(15 - 11)`

`m = (18\%)/(4)`

`m = 4.5\%`

`m = 0.045`

The equation for x years after 2000 is:

`y = m(x - x_1) + y_1`

`y = 0.045(x - 11) + 5\%`

`y = 0.045x - 0.495 + 0.05`

`y = 0.045x -0.445`