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24. Congratulations! You have just won a jet ski worth $8000. The depreciated value of the jet ski (V) after t years is given by V = 8000 − 725t , 0 ≤ t ≤ 11.
a. Use a graphing utility to graph the equation. Include a t-chart with at least 5 key points with your accurate labeled graph.
b. After how many years will the jet ski be worth $5100? Show all of your work or explain how you came up with your answer.
c. What will be the value of the jet ski after 9 years? Show all of your work or explain how you came up with your answer.



Answer :

a) [tex]y=mx+c[/tex]
[tex]m=gradient=-725[/tex]
[tex]y(v)-intercept=8000[/tex]

b) [tex]5100=8000-725t[/tex]
[tex]2900=725t[/tex]
[tex]t=4[/tex]
The value will be 5100 after 4 years.

c) [tex]V=8000-725(9)[/tex]
[tex]V=8000-6525[/tex]
[tex]V=1475[/tex]
The value of the jet will be 1475 after 9 years.

Hope I helped bro, now i can sleep
So:

[tex]V=8000-725t\quad \{ 0\le t\le 11\} [/tex]

*V (in dollars) stands for the depreciated or non depreciated value of the jet ski.

*t (in years) stands for the amount of time that has passed. t is greater or equal to 0 and less than or equal to 11.

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Question (a):

Now V is a function of t. V=f(t).

When t=0, V=0 --> Point:(0,0)

When t=2, V=6550 -->  Point (2, 6550)

When t=4, V=5100 --> Point (4, 5100)

When t=6, V=3650 --> Point (6, 3650)

When t=8, V=2200 --> Point (8,2200)

When t=11, V=25  --> Point: (11, 25)

So as the graph V=8000-725t is LINEAR, we can draw a line through the points mentioned above.

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Question (b): After how many years will the jet ski be worth $5100?

[tex]8000-725t=5100\\ \\ 8000-5100=725t\\ \\ 2900=725t\\ \\ \frac { 2900 }{ 725 } =t\\ \\ \therefore \quad t=4,\quad when\quad V=5100[/tex]

Answer: 4 years.

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Question (c): What will be the value of the jet ski after 9 years?

[tex]When\quad t=9,\\ \\ V=8000-725\left( 9 \right) \\ \\ =1475[/tex]

The answer is $1,475.00

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