Question

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

Answer 1

Answer:

$1500

Step-by-step 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! :)

Answer 2

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.

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