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You buy a new stereo for $1300 and are able to sell it 4 years later for $275. Assume that the resale value of the stereo decays exponentially with time. Write an equation giving the resale value $V$ (in dollars) of the stereo as a function of the time $t$ (in years) since your bought it. Round all decimals to four decimal places.

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Answer:

[tex]V=P(0.6782)^t[/tex]

Step-by-step explanation:

Let V be the future value, P the present value, t be time and x the rate of change expressed as:

[tex]V=Px^t, V=275,P=1300,t=4\\\\275=1300x^4\\\\x^4=\frac{275}{1300}\\\\x=0.6782\\\\\therefore V=P(0.6782)^t[/tex]

Hence, the resale value of the stereo as a function of time is [tex]V=P(0.6782)^t[/tex]

The equation that provides the resale value should be [tex]V = P(0.6782)^t[/tex]

Calculation of an equation:

Since You buy a new stereo for $1300 and are able to sell it 4 years later for $275.

So,

[tex]275 = 1300x^4\\\\x^4 = 275\div 1300\\\\x = 0.6782[/tex]

Hence, The equation that provides the resale value should be [tex]V = P(0.6782)^t[/tex]

Learn more about an equation here: https://brainly.com/question/24334745

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