Exponential depreciation model for Tessa’s T-shirt printing machine — value x years after purchase (initial $2,200, loses 1/4 per year)

Find the exponential equation for the value of Tessa's T-shirt printing machine that starts at $2,200 and loses one-quarter of its value each year. Model in the form y = a(b)^x with a and b as numbers.

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Start with the initial value: a = $2,200.

If the machine loses 1/4 of its value each year, it retains 1 - 1/4 = 3/4 of its value each year. That retention factor is b = 3/4 (which is 0.75 as a decimal).

The exponential model in the form y = a(b)^x is therefore:

y = 2200(3/4)^x

You can also write it with a decimal base: y = 2200(0.75)^x.

Check: after 1 year, y = 2200(3/4) = 1650; after 2 years, y = 2200(3/4)^2 = 1237.50, which matches repeated 25% reductions.

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