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Sagot :
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:
[tex]A(t) = A(0)(1 - r)^t[/tex]
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:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 1500(1 - 0.25)^t[/tex]
[tex]A(t) = 1500(0.75)^t[/tex]
In 8 years, the value will be given by:
[tex]A(8) = 1500(0.75)^8 = 150.17[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
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