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1. 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

Respuesta :

Hi!

Samuel bought the mixer for $54,205. The value of this (the prive) decreases every year at a costant rate (so, for example, it may decrease of $100 every year).

we are solving for t and we should keep in mind that we multiply the price for the function (1 - rate/100)^time

in f(t) you put the value of year 1 for example

[tex]f(t) = 54205(1- \frac{value1-value2}{value1}) ^t[/tex]

Solving for r will bring us to the solution, and we can substitute 1 to t since we are calculating how much it decreases after ONE year.

We would divide for 54205 to cancel out that 54205 multiplicating the parenthesis.

Also, the x is given by the formula (vale2-value1)/value1 to see how much the price changes from year 1 to year 2

We will get [tex] f(t) = 54205(\frac{(47000-41000)}{47000}) ^1[/tex]

Again, it would be:

f(t) = 54205(0.13)^1
JeanaShupp

Answer: [tex] f(x)=54205(0.87)^t[/tex]

Step-by-step explanation:

Given: The initial value of cement mixer (A) = $54,205

After one year, the value of mixer = $47,158.35

The constant rate of depreciation (b)=[tex]\frac{47158.35}{54205}=8.7[/tex]

The exponential function represent the value after depreciation of t years is given by :-

[tex]f(t)=A(b)^t\\\\\Rightarrow\ f(x)=54205(0.87)^t[/tex]

Hence, the function best represents the value of the cement mixer after t years will be

[tex] f(x)=54205(0.87)^t[/tex]

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