A print shop purchases a new printer for $25,000. The equipment depreciates at a rate of 5% each year. The relationship between the value of the printer, y, and the year number, x, can be represented by the equation, y = 25,000 • 0.95 x . Complete the table below with the value of the printer, to the nearest cent, in years 1, 2, and 3. Include proper commas and decimals in your answer.
Accepted Solution
A:
Answer:Part 1) For x=1 year, [tex]y=\$23,750[/tex] Part 2) For x=2 years, [tex]y=\$22,562.50[/tex] Part 3) For x=3 years, [tex]y=\$21,434.38[/tex] Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]y=P(1-r)^{x}[/tex] where
y is the depreciated value
P is the original value
r is the rate of depreciation in decimal x is the number of years in this problem we have
[tex]P=\$25,000\\r=5\%=0.05[/tex]
substitute[tex]y=25,000(1-0.05)^{x}[/tex] [tex]y=25,000(0.95)^{x}[/tex] Part 1) Find the value of the printer, to the nearest cent, in year 1soFor x=1 yearsubstitute in the exponential equation[tex]y=25,000(0.95)^{1}[/tex] [tex]y=\$23,750[/tex] Part 2) Find the value of the printer, to the nearest cent, in year 2soFor x=2 yearssubstitute in the exponential equation[tex]y=25,000(0.95)^{2}[/tex] [tex]y=\$22,562.50[/tex] Part 3) Find the value of the printer, to the nearest cent, in year 3soFor x=3 yearssubstitute in the exponential equation[tex]y=25,000(0.95)^{3}[/tex] [tex]y=\$21,434.38[/tex]