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meriva
2 years ago
9

Samuel bought a cement mixer for $54,205. The value of the cement mixer depreciated at a constant rate per year. The table 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.
Mathematics
1 answer:
Paul [167]2 years ago
8 0

The value of cement mixer after t year is f(t) = 54,205(0. 87)^{t}

Given to us

The value of cement mixer when bought, P= $ 54,205

the value of cement mixer after 1 year, P_1=   $ 47,158. 35

the value of cement mixer after 2 year,P_2=  $ 41,027. 76

To find out depreciation we can use the formula for depreciation,

P_n= P(1-r)^n\\where,\\P_n= Value\ of\ asset\ after\ n\ year\\P= Value\ of\ asset\ when\ bought\\r= rate\ of\ depreciation\\n= number\ of\ years

By putting the value, in the formula we get,

P_1= P(1-r)^n\\\\47,158.35= 54,205\times (1-r)^1\\\\\dfrac{47,158.35}{54,205} = (1-r)\\\\0.87=1-r\\\\r=0.13

Therefore, putting the value of r and P in depreciation formula for t years we get,

P_n= P(1-r)^n

f(t) = 54,205(0. 87)^{t}

Hence, the value of cement mixer after t year is f(t) = 54,205(0. 87)^{t}.

To know more visit:

brainly.com/question/3023490

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