James is interested in buying a new cadillac escalade. He did some research and found out thy on average the suv will cost 40,057.07 after 2 years of the purchase, and 19,192.53 after 5years. Find a rule that shows the depreciation of the vehicle. How much was the brand new cadillac escalade? What is its depreciation rate (multiplier)
let the depreciation rate be r
and the initial cost be a
looks like a geometric sequence where
ar^5 = 19 192.53 and ar^2 = 40 057.07
divide first by the second
r^3 = .4791296
take cube root
r = .7825 ( it depreciates at a rate of 21.75% per year)
sub that back into ar^2 = ...
a = 65 420
(Somebody should talk some sense into James)
Lol thanks
To find the rule that shows the depreciation of the Cadillac Escalade, we can use the given information.
Let's assume the initial cost or purchase price of the brand new Cadillac Escalade is represented by 'P' dollars.
After 2 years, the Cadillac Escalade is worth $40,057.07, which means it has lost the initial cost minus $40,057.07. Therefore, the depreciation after 2 years is P - $40,057.07.
Similarly, after 5 years, the Cadillac Escalade is worth $19,192.53. So, the depreciation after 5 years is P - $19,192.53.
From this information, we can set up two equations:
Depreciation after 2 years: P - $40,057.07 = ?
Depreciation after 5 years: P - $19,192.53 = ?
To find the initial cost or purchase price, we need to solve one of the equations for 'P'.
Subtracting $40,057.07 from both sides of the first equation, we get:
P = $40,057.07
Therefore, the initial cost or purchase price of the brand new Cadillac Escalade is $40,057.07.
To find the depreciation rate (multiplier), we can calculate the ratio of the depreciation to the initial cost.
Depreciation rate (multiplier) = (Depreciation/Initial Cost)
Depreciation rate (multiplier) after 2 years = (P - $40,057.07)/P
Depreciation rate (multiplier) after 2 years = ($40,057.07/$40,057.07) = 1
Depreciation rate (multiplier) after 5 years = (P - $19,192.53)/P
Depreciation rate (multiplier) after 5 years = ($19,192.53/$40,057.07) ≈ 0.4796 (rounded to four decimal places)
Therefore, the depreciation rate (multiplier) after 2 years is 1, and after 5 years, it is approximately 0.4796.