Question

Leo bought a bulldozer for $63,103. The value of the bulldozer depreciated at a constant rate per year. The table below shows the value of the bulldozer after the first and second years: Year 1 2 Value (in dollars) 58,054.76 53,410.38 Which function best represents the value of the bulldozer after t years?

Answer 1

Year 1
58054.76=63,103(1-r)^1
Year 2
53,410.38=63103(1-r)^2

Answer 2

`A=63103(0.92)^t`

Explanation:

Since, the decay function that show the value is decreasing by a constant rate,

`A=P(1-r)^t`

Where,

P = initial value,

r = rate per period,

t = number of periods,

According to the question,

P = $ 63,103,

When t = 1, A = 58054.76

`\implies 58054.76=63103(1-r)`

`\implies 0.92 = 1 - r`

Hence, the function that represents the value of the bulldozer after t years,

`A=63103(1-r)^t=63103(0.92)^t`