Question

Rate of Change , you are given the dollar value of a product in 2004 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

(Let t=0 represent 2000.)

2004 value= $156 with $4.50 increase per year
...?

Answer 1

when t=4, v = 156the equation of linear liney = mx+bm=slopeb = y-intercept or initial valueapply it to this problemv = 4.5t + bto solve for b, use given info (v=156 when t=4)156 = 4.5(4) + bb = 156 - 4.5(4)b = 156 - 18b = 138
Linear equation:v = 4.5t +138this means the product had value of $138 in 2000

Answer 2

The linear equation is v = 4.5t +138

The product had value of $138 in 2000.

Explanation:

In 2004, dollar value(v) = $156 and rate of change (m) = $4.50

The linear equation is in the form of y = mx + b, where "m" is slope or rate of change, b is the y-intercept.

We can rewrite the equation as v = m(t) + b.

Now let's find the value of b, when t = 4, m = 4.5, v = 156

156 = 4.5(4) + b

b = 156 - 4.5(4)

b = 156 - 18

b = 138

So, the linear equation is v = 4.5t +138

When t=0, the dollar value (v) = 4.5(0) + 138

v = $138

So, the product had value of $138 in 2000