Q:

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]