Hi! I really do not get how to solve the initial value problem.
Bryan comes up a new strategy to get familiar with the fox. He decides that he decreases
the distance such that the rate of change is exactly ln 5 times of the actual distance. Bryan estimates that right now the fox is 127 m away. Set up and solve the initial value problem!
How much day has Bryan have to wait get friendly (<1m distance) with the fox?
the rate of change is exactly ln 5 times of the actual distance
so, if s is the distance,
ds/dt = ln5 s
ds/s = ln5 dt
lns = ln5 t + ln c
s = e^(ln5 t + ln c) = c*(e^ln5)^t = c*5^t
at t=0, s=127, so
s = 127*5^t
so find t when s < 1
1 < 127 * 5^t
1/127 < 5^t
-ln127 < t ln5
t > -ln127/ln5