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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

Verified Answer :

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

Answer:

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

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




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