SOLUTION: If the number of soap, N, in two baths are modeled by N_a=3000e_{^{0.09t}}\:\:N_b=5000e^{kt}, where 't' is the number from midday. find the value of 'k' for the second bath that wi

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If the number of soap, N, in two baths are modeled by N_a=3000e_{^{0.09t}}\:\:N_b=5000e^{kt}, where 't' is the number from midday. find the value of 'k' for the second bath that wi      Log On


   

Question 1172513: If the number of soap, N, in two baths are modeled by N_a=3000e_{^{0.09t}}\:\:N_b=5000e^{kt}, where 't' is the number from midday. find the value of 'k' for the second bath that will have the number of soap in the two baths being equal at 7:00pm.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
3000e^(0.09t)=5000e^(kt); t=7
e^(0.63)=(5/3)e^(7k)
e^(0.63-7k)=(5/3)
ln both sides
0.63-7k=0.5108
7k=0.1192
k=0.0170