Write A Linear Equation

[nycmathguy]

In Exercises 91 and 92, you are given
the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 16 represent 2016.)


91. Value for 2016: $3000; Rate: $150 decrease per year.

I see the point (16, 3000) = (t, V).

y - V_1 = -150(t - t_1)

y - 3000 = -150(t - 16)

y = -150t + 2400 + 3000

y = -150t + 5400

Correct?

92. Value for 2016: $200; Rate: $6.50 increase per year.

For this problem, I see the point (16, 200) = (t, V)

y - 200 = 6.5(t - 16)

y = 6.5t - 104 + 200

y = 6.5t + 96

Correct?

 

[nycmathguy]

Value for 2016: $3000; Rate: $150 decrease per year

V=150t+c
when t=16, V=3000
3000=150*16+c
3000=2400+c
3000-2400=c
c = 600

V=150t+600=>the dollar value V of the product in terms of the year t

expected to change during the next 5 years:

t=16+5=21

V=150*21+600
V=3750

I got the right answer for 91. Question 92 is an even number question and thus not listed in the back of the book.

Book's answer for 91:

V(t) = −150t + 5400, 16 ≤ t ≤ 21

 

[MathLover1]

Value for 2016: $3000; Rate: $150 decrease per year


$150 decrease per year (sorry, didn't pay close attention to "decrease")

V=-150t+c
when t=16, V=3000
3000=-150*16+c
3000=-2400+c
3000+2400=c
c = 5400

V=-150t+5400=>the dollar value V of the product in terms of the year t

 

[nycmathguy]

This means I got it right.

 

[MathLover1]

This means I got it right.

yes you did

 

[nycmathguy]

yes you did

Perfect. I think this site is going to work for us.