The depreciation rate, r, for a $50,000 news car is given by the function r = 1 - (V/50,000)^(1/5), where V is the value of the car when it is five years old.
a) What is the depreciation rate for a $50,000 BMW that is worth $28,000 after 5 years? (I already found the answer to this: 10.95%)
b) Write V as a function of r (Help me answer this part!)
Thank you!
(V/50,000)^(1/5) = 1-r
V/50,000 = (1-r)^5
V = 50,000 (1-r)^5
What did you do with the exponent?
how do you do part a?
Steph, I raised both sides of the equation to the fifth power.
Anonymous
r = 1 - (28/50)^.2
= 1 - .56^.2
= 1 - .89
= .1095 or 10.95%
Thank you!!
To write V as a function of r, we need to rearrange the given equation:
r = 1 - (V/50,000)^(1/5)
Let's solve this equation for V.
1 - r = (V/50,000)^(1/5)
Raise both sides of the equation to the power of 5:
(1 - r)^5 = ((V/50,000)^(1/5))^5
Simplifying:
(1 - r)^5 = V/50,000
Multiply both sides of the equation by 50,000:
50,000 * (1 - r)^5 = V
Therefore, V can be written as a function of r:
V = 50,000 * (1 - r)^5
Now you can use this equation to calculate V for any given depreciation rate, r.