Question

Based on her past experiences, a homeowner estimates that appliances lose 25% of their resale value each year. If her estimate is accurate, how much will an appliance currently valued at $1,500 be worth in 8 years?

Answer 1

Using an exponential function, it is found that an appliance currently valued at $1,500 will be worth $150.17 in 8 years.

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

In this problem, we have that:

• The appliance is currently valued at $1,500, hence A(0) = 1500.

• It loses 25% of their resale value each year, hence r = 0.25.

Thus, the equation is given by:

$A(t) = A(0)(1 - r)^t$

$A(t) = 1500(1 - 0.25)^t$

$A(t) = 1500(0.75)^t$

In 8 years, the value will be given by:

$A(8) = 1500(0.75)^8 = 150.17$

More can be learned about exponential functions at https://brainly.com/question/25537936

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