Answer:
[tex]V(x) = -\frac{340}{3}x +2220[/tex]
[tex]V(8) = 1313.3[/tex]
Step-by-step explanation:
Given
Let x represent years and V represents the value.
So, we have:
[tex](x_1,v_1) = (0,2220)[/tex]
[tex](x_2,v_2) = (6,1540)[/tex]
Solving (a): The linear function
First, we calculate the slope (m)
[tex]m = \frac{v_2 - v_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{1540-2220}{6-0}[/tex]
[tex]m = \frac{-680}{6}[/tex]
[tex]m = -\frac{340}{3}[/tex]
The linear function is calculated using:
[tex]v - v_2 = m(x - x_2)[/tex]
Where:
[tex](x_2,v_2) = (6,1540)[/tex]
[tex]m = -\frac{340}{3}[/tex]
So, we have:
[tex]v - 1540 = -\frac{340}{3}(x - 6)[/tex]
Open bracket
[tex]v - 1540 = -\frac{340}{3}x +\frac{340}{3}* 6[/tex]
[tex]v - 1540 = -\frac{340}{3}x +680[/tex]
Make v the subject
[tex]v = -\frac{340}{3}x +680+1540[/tex]
[tex]v = -\frac{340}{3}x +2220[/tex]
So, the function is:
[tex]V(x) = -\frac{340}{3}x +2220[/tex]
Solving (b): When x = 8
Substitute 8 for x in [tex]V(x) = -\frac{340}{3}x +2220[/tex]
[tex]V(8) = -\frac{340}{3}*8 +2220[/tex]
[tex]V(8) = -\frac{340*8}{3} +2220[/tex]
[tex]V(8) = -\frac{2720}{3} +2220[/tex]
Take LCM
[tex]V(8) = \frac{-2720+2220*3}{3}[/tex]
[tex]V(8) = \frac{-2720+6660}{3}[/tex]
[tex]V(8) = \frac{3940}{3}[/tex]
[tex]V(8) = 1313.3[/tex]
Hence, its value after 8 years is 1313.3
