Question

Samuel bought a cement mixer for $54,205. The value of the cement mixer depreciated at a constant rate per year. The table below shows the value of the cement mixer after the first and second years:

Year 1 2 Value (in dollars) 47,158.35 41,027.76

Which function best represents the value of the cement mixer after t years?

f(t) = 47,158.35(0.87)t
f(t) = 54,205(0.13)t
f(t) = 47,158.35(0.13)t
f(t) = 54,205(0.87)t

Answer 1

the last one is the correct answer. f(t)=54,205(0.87)t

Answer 2

`f(t)= 54,205(0.87)^t`

Step by step explanation

Year 1 2

Value (in dollars) 47,158.35 41,027.76

Initial value of cement mixer = $54,205

For depreciation we use formula y=ab^t

Where 'a' represents the initial value

b is the rate of depreciation

t is the number of years

initial value = 54,205 so a=54,205

When t=1 then y = 47,158.35

We plug in the values in the formula and find out 'b'

`y=a(b)^t`

`47158.35=54205(b)^1`

Divide by 54205 on both sides

b= 0.87

a= 54,205

So function becomes
`f(t)= 54,205(0.87)^t`