Question 437335
The linear function will have the general form
V(t) = at + b 
where a and b are constants
Given: V(2) = 1500, V(10) = 300
So we have the following two equations:
1500 = 2a + b (1)
300 = 10a + b (2)
This gives us two equations in two unknowns, a and b.
By subtracting (2) from (1) we can eliminate b:
1200 = -8a -> a = -150
Now use one of the two equations above to solve for b:
Using (1), we get
1500 = -300 + b -> b = 1800
So, our equation is:
V(t) = -150t + 1800
So the value after 5 years is:
V(5) = -150(5) + 1800 = $1050
The time when the equipment will have a value of $100 is given by:
100 = -150t + 1800
Solve for t:
t = -1700/-150 = 11.33 years
The graph is shown below:
{{{graph(300,300,-20,20,-2000,2000,-150x + 1800)}}}