Depreciation problem: please help

[roxstar1]

Depreciation: after t years, the value of a car purchased for $20,000 is
v(t)= (20,000)(3/4)^t


b) find the rate of change of v with respect to t, when t=1 and t=4

v'(t) = (20,000)(ln (3/4))(3/4t)
v'(1) = (20,000)(ln (3/4))((3/4)(1))
v'(1) = -4315.231
v'(4) = (20,000)(ln (3/4))((3/4)(4))
v'(4) = -17260.824

Im having trouble with part c now, so I am not sure if I have done part b correctly

c) graph v'(t) and determine the horizontal assymptote of v'(t). Interpret its meaning in the context of the problem.

everytime I graph my v'(t) I get a straight, slanted line. I cannot identify any horizontal assymptotes... any suggestions would be much appreciated.

 

[Gene]

Error in v'(t)
v=k(r)^t
ln(v)=ln(k)+t*ln(r)
dv/v=ln(r)dt
v'=v*ln(r) =k*r^(t)*ln(r)
or in this
v'(t)= (20,000)(3/4)^t*ln(3/4)

You should have been suspicious when it depreciated more in the fourth than it was worth at the end of the first year.