Between 7:00 AM and 8:00 AM, trains arrive at a subway station at a rate of 12 trains per hour (0.2 trains per minute). The following formula from statistics can be used to determine the probability that a train will arrive within t minutes of 7:00 AM. F(t)=1-e^-0.2t. Determine how many minutes are needed for the probability to reach 60%.
Trying to use formula Y=C^(k*x)
Y is the output, C is initial, K is %, and x is time.

Question

Between 7:00 AM and 8:00 AM, trains arrive at a subway station at a rate of 12 trains per hour (0.2 trains per minute). The following formula from statistics can be used to determine the probability that a train will arrive within t minutes of 7:00 AM. F(t)=1-e^-0.2t. Determine how many minutes are needed for the probability to reach 60%.
Trying to use formula Y=C^(k*x)
Y is the output, C is initial, K is %, and x is time.

anonymous · Answer

In case someone else gets this:
1-e^-.08t=.6  (.6 is the 60%), then minus 1 from each side,
-e^-.08t=-.4  , now divide off the negatives
e^-.08t=.4   , now get rid of e with it's inverse of ln to both sides
-.08t=ln(.4)  , the divide the -.08 to each side and use calculator
t= ln(.4)/(-.08)
t = approximately 11 minutes. Hopefully someone can use this formula to solve like problems.