Let's go through each question and check your work.
a) Finding the rate of depreciation:
To find the rate of depreciation, we divide the change in value by the number of years. In this case, the change in value is $60,000 - $12,000 = $48,000 over 4 years. Dividing $48,000 by 4 gives us a rate of depreciation of $12,000 per year. So your answer, -12,000, is correct.
b) Finding the linear equation expressing the system's book value at the end of t years:
To find the linear equation for the book value, we start by using the general form of a linear equation: y = mx + b, where y represents the book value at the end of t years, x represents the number of years, m represents the rate of depreciation, and b represents the initial value.
In this case, the initial value (b) is $60,000, and the rate of depreciation (m) is -12,000. Plugging these values into the equation, we get:
y = -12,000x + 60,000
So the correct linear equation expressing the system's book value at the end of t years is y = -12,000x + 60,000. Your answer, v = -12,000x + 0, is incorrect because you left out the initial value of $60,000.
c) Finding the system's book value at the end of the third year:
To find the book value at the end of the third year, we substitute t = 3 into the linear equation we found in part b:
v = -12,000(3) + 60,000
= -36,000 + 60,000
= 24,000
So the correct book value at the end of the third year is $24,000. Your answer, -36,000, is incorrect as you made a sign error while substituting the value of t into the equation.
Overall, your answer for part a is correct, but there are errors in parts b and c. The correct answers for parts b and c are:
b) The linear equation expressing the system's book value at the end of t years is v = -12,000t + 60,000.
c) The system's book value at the end of the third year is $24,000.