MATH SOLVE

3 months ago

Q:
# BRAINLIESTTTTT!!!!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 2Value (in dollars) 47,158.35 41,027.76Which 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

Accepted Solution

A:

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

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