You just bought a new car for $22,000.Assume that the value of your new car depreciates at a constant 12 % per year

You just bought a new car for $22,000.Assume that the value of your new car depreciates at a constant 12 % per year

Question
Modeling
asked 2021-01-25

You just bought a new car for $22,000. Assume that the value of your new car depreciates at a constant \(12\ \%\) per year.

1) The decay rate is square

2) The decay factor is square

3) The equation of the function that represents the value, V(t), of the car in dollars t years from now is \(V\ =\ \Box\) (Write an expression that completes the function's equation.)

Answers (1)

2021-01-26

Step 1 Given that the value of the car depreciates at a constant \(12\ \%\) per year.

That means the decay \(rate = r = 12\ \% = 0.12\) The decay factor is\(b = 1\ −\ r = 1\ −\ 0.12 = 0.88\)

Step 2 Given that the initial value is $22000 That means \(a = 22000\)

And the decay factor\(= b = 0.88\) So the equation of the function is: \(V(t) = a(b)^{t}\)
\(V(t) = 22000(0.88)^{t}\)

Answer(1): \(0.12\)

Answer(2): \(0.88\)

Answer(3): \(22000(0.88)^{t}\)

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