Question

After 2 years, a boat has a value of $36000. After 8 years, its value is $9000. Assuming a linear function, write an equation in the form v(t)=mt+b that shows the value of the boat, v(t), after t years of depreciation.

Answer 1

v(t) = -4500t + 45000

Explanation:

Slope of line = (9000−36000)/(8−2) = −27000/6 = −4500; using point-slope form with (2, 36000) gives y − 36000 = −4500(x−2), which yields y = −4500x + 45000, which is v(t) = −4500t + 45000 in function notation.

Answer 2

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Therefore our line so far can be written as:

`Value(t) = -4500 t + b`

in order to find the vertical intercept, we evaluate the line at one of the given points, for example at (2, 36000):

`36000 = -4500 (2) + b`

`36000 = -9000 + b`

therefore, b = 36000 + 9000 = 45000

The line is :
`Value (t) = - 4500 t + 45000`