Question 1092545: The onlookers gazed in excitement as the number of gremlins decreased exponentially. When they were first observed, there were 48, but in only 50 minutes they had decreased to 42. How long would it take before the gremlins decreased to 25?
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! If there is continuous decreasing, then P_1=P_0*e^-kt, where P_0 is the initial population, P_1 is the resulting population, k is a constant, and t is the time, in minutes. So:
42=48e^-50k
.875=e^-50k
ln 0.875=ln e^-50k=-50k ln e=-50k
k=-ln 0.875/50=0.0027
Then
25/48=0.52083
so
0.52083=e^-0.0027t
ln 0.52083=ln e^-0.0027t=-0.0027t ln e=-0.0027t
t=ln 0.52083/-0.0027=241.6 minutes until there are only 25 gremlins left
☺☺☺☺
|
|
|
