Question

A new car is purchased for $47, 000 and over time its value depreciates by one half

every 4.5 years. What is the value of the car 23 years after it was purchased, to the
nearest hundred dollars?

Answer 1

we know the car depreciates every 4.5 years, and we also know its by one half or namely the depreciation rate is 50% of its value.

`\textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{(t)/(c)}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &47000\\ r=rate\to 50\%\to (50)/(100)\dotfill &0.5\\ t=years\dotfill &23\\ c=period\dotfill &4.5 \end{cases} \\\\\\ A=47000(1 - 0.5)^{(23)/(4.5)}\implies A=47000(0.5)^{(46)/(9)}\implies A\approx 1400`

Answer 2

$1500

Explanation:

you can figure it out by going in increments of 4.5 years because that is the info you have from the problem so

47000 4.5 years later is 23500

9 years = 11750

13.5y = 5875

18y = 2937.5

22.5 years later is 1468.75

22.5 years is about 23 years and to the nearest hundred dollars that is $1500 so that is the answer

Hope this helps! :)