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? (5 points)

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

Do you know the basic formula for this question?

Answer 2

.. okay so if you ever come back, the general formula is described as shown:
\[\Large y=a(1+r)^t \]

Answer 3

This is salvage value vs depreciation value. The life of this so called "cement mixer" is 8.25 to 8.50 years. So with all of this information you now know how would you go about using @luigi0210 's equation in order to obtain your answer?

Answer 4

Well, just to finish it. You are given a, which is the initial value as $47,158.35. The t will stay as t since no time is given. The rate can be calculated using the two amounts provided in year 1 and year 2, soo:
\[\large \frac{47,158.35-41,027.76}{47,158.35} = 0.13\]

So now you have the r value as 0.13, and the initial amount as $47,158.35.
Just plug all this information into the provided equation and you will get this:
\[\large y= 47,158.35(1-0.13)^t \]

It is -0.13 because it DEPRECIATES over time.