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

Answer:

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

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

Step-by-step 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