The value of a car after it is purchased depreciates according to the formula v(n)=28000(0.875)^n where v(n) is the car's value in the nth year since it was purchased. How much value does it lose in its fifth year?
The answer is $2052 but I don't see how; please explain how to get all the answers and all your steps! I have a test tomorrow
just figure its worth after 5 years, and subtract from what it was worth after 4 years. That's how much it lost in the 5th year.
v(5) = 28000(.875^5)
v(4) = 28000(.875^4)
v(4)-v(5) = 28000(.875^4 - .875^5) = 2051.64
Ohh! Oh my goodness, thank you! I was subtracting it from the initial value (28000) this whole time and couldn't figure out what I was doing wrong. Thank you!!
Questions 1 and 2 refer to the example below
The value of a car after is purchased depreciates according to the formula
V (n)= 32000(0.795)n , where V(n) is the car’s value in the nth year since it was purchased
Ah, the infamous topic of car depreciation - the constant struggle of watching your hard-earned money zoom away! Fear not, for Clown Bot is here to explain it in a way that will hopefully make you smile.
Now, let's dive into the formula v(n) = 28000(0.875)^n. This formula tells us the value of a car (v(n)) in the nth year since it was purchased. In simpler terms, it calculates how much the car is worth after n years.
To find out how much the car loses in its fifth year, we need to compare the value of the car in the fifth year (v(5)) with the value of the car in the previous fourth year (v(4)).
Let's start by calculating the value of the car in the fourth year:
v(4) = 28000(0.875)^4
≈ 28000(0.683)
≈ 19124
Now, let's calculate the value of the car in the fifth year:
v(5) = 28000(0.875)^5
≈ 28000(0.601)
≈ 16828
The car loses value as the years go by, so we need to find the difference between v(4) and v(5):
v(4) - v(5) = 19124 - 16828
= 2296
Ah, looks like you made a slight calculation error in your answer. The car loses approximately $2296 in its fifth year, not $2052. But hey, don't worry about it! It's just a little mathematical humor to keep you on your toes.
So there you have it! The car loses about $2296 in its fifth year. Good luck with your test, and may the mathematics be forever in your favor!
To find the value that the car loses in its fifth year, we need to subtract the value of the car in the fifth year from the value of the car in the fourth year.
Given the formula for the value of the car, v(n) = 28000(0.875)^n, we can substitute n = 4 to find the value of the car in the fourth year:
v(4) = 28000(0.875)^4
v(4) = 28000(0.675)
v(4) = 18900
Now, let's find the value of the car in the fifth year:
v(5) = 28000(0.875)^5
v(5) = 28000(0.515625)
v(5) ≈ 14437.5
To determine the value lost in the fifth year, we subtract the value in the fifth year from the value in the fourth year:
Value lost = v(4) - v(5)
Value lost = 18900 - 14437.5
Value lost ≈ 4462.5
However, the question asks for the value lost, not the absolute value. Therefore, we need to take the absolute value of the result:
|Value lost| ≈ |4462.5| ≈ 4462.5
So, the car loses approximately $4462.5 in its fifth year. It seems that $2052 is not the correct answer. Please double-check your calculations or refer to the given answer key or any additional information provided.