Answer :
Answer:
a) V(0) = $15,000
b) r = -$5350.124*(0.7)^t
Step-by-step explanation:
Given:
- The value of car as a function of time t in years:
V = 15,000*(0.7)^t
Find:
a) What are the initial cost V_I
b) the rate of depreciation r
Solution:
- The initial cost can be computed by setting t = 0 in the given relation. We will get the original cost of car before it started depreciating annually.
V(0) = 15,000*(0.7)^0
V(0) = $15,000
- The depreciation rate 'r' of the car can be evaluated by taking a derivative of V with respect to time t. That is rate of change of V with respect to time or the rate at which the value of car decreases:
dV/dt = r
r = d(15,000*(0.7)^t) / dt
r = 15,000*(0.7)^t * Ln (0.7)
r = -5350.124159*(0.7)^t
- We see that the depreciation rate r is also a function of time t in year. Every year the depreciation rate itself changes.
Answer:
Initial cost (i) = 15,000
Rate of depreciation r = 0.3
Step-by-step explanation:
To solve this we apply the exponential decay function
Y = i(1-r)^t
i = initial amount
r = depreciation/decay rate
t = time interval
y= 15000(0.7)^t
Where y = i(1-r)^t
Therefore from the equation
Initial cost (i) = 15,000
Rate of depreciation r =
1 - r = 0.7
r = 1 - 0.7
r = 0.3