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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.)

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dfrancolopera

Answer:

[tex]V=r*t+D-2*r[/tex]

with

[tex]V=[/tex] dollar value of the product

[tex]r=[/tex] value's rate of change

[tex]t=[/tex] time in years (where t=0 represents 2010)

[tex]D=[/tex] dollar value of product in 2012

Step-by-step explanation:

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

[tex]V=r*t+C[/tex] (equation 1)

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

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

[tex]V=r*t+C[/tex] (equation 1)

[tex]D=r*2+C[/tex]

[tex]C=D-2*r[/tex]

So the final equation would be

[tex]V=r*t+D-2*r[/tex]

with

[tex]V=[/tex] dollar value of the product

[tex]r=[/tex] value's rate of change

[tex]t=[/tex] time in years (where t=0 represents 2010)

[tex]D=[/tex] dollar value of product in 2012

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