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Sloan [31]
3 years ago
12

A car purchased for $24,000 is expected to lose value, or depreciate, at a rate of 8% per year. This situation can be modeled by

P(t)=24,000(1-0.08)^t
What is the meaning of the output P(t) in context of the problem?
What is the meaning of the input t in context of the problem?
Mathematics
1 answer:
algol [13]3 years ago
5 0

\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &24000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{current value}}{\stackrel{A}{\stackrel{\downarrow }{P(t)}}}=24000(1-0.08)^{\stackrel{\stackrel{\textit{years}}{\downarrow }}{t}}

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4 0
3 years ago
Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.
Paul [167]

Answer:

5 rad

Step-by-step explanation:

Recall that the length of an arc of circumference is given by the formula:

Arc\,Length=\theta\,*\,radius, where \theta is the subtended angle [in radians] from the circumference's center.

Therefore in this case, you know the arc length (81.5 cm), and the radius (16.3 cm), and can solve for the angle \theta using the above equation as shown below:

Arc\,Length=\theta\,*\,radius\\81.5\,cm = \theta\,*\,16.3\,cm\\\frac{81.5}{16.3} = \theta\\\theta=5\,rad

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Answer:

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