Question

You are given the dollar value of a product in 2012 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 represent 2010.)

Answer 1

`V=r*t+D-2*r`

with

`V=` dollar value of the product

`r=` value's rate of change

`t=` time in years (where t=0 represents 2010)

`D=` dollar value of product in 2012

Explanation:

A linear equation for V in terms of t will have the following form

`V=r*t+C` (equation 1)

where
`r` will be the rate at which the value of the value of product is expected to change,
`V` is the dollar value of the product at the year
`t` (being
`t=0` for 2010) and
`C` is a constant number which we should be able to find knowing the value of
`V` at some point in time.

Let's call
`D` the dollar value of the product in 2012, we can replace this value in the equation 1 in order to find
`C`

`V=r*t+C` (equation 1)

`D=r*2+C`

`C=D-2*r`

So the final equation would be

`V=r*t+D-2*r`

with

`V=` dollar value of the product

`r=` value's rate of change

`t=` time in years (where t=0 represents 2010)

`D=` dollar value of product in 2012