SOLUTION: The function below describes the market penetration of a product, where p, q, and C are constants. Solve for C when f(0)=0. {{{ f(t)=(q-pe^(-(t+C)*(p+q)))/(q*(1+e^(-(t+C)*(p+q))))

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The function below describes the market penetration of a product, where p, q, and C are constants. Solve for C when f(0)=0. {{{ f(t)=(q-pe^(-(t+C)*(p+q)))/(q*(1+e^(-(t+C)*(p+q))))       Log On


   

Question 1113186: The function below describes the market penetration of a product, where p, q, and C are constants. Solve for C when f(0)=0.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If f%280%29=0, then the numerator must equal zero.
q-pe%5E%28-%28C%29%2A%28p%2Bq%29%29%29=0
q=pe%5E%28-%28C%29%2A%28p%2Bq%29%29%29
q%2Fp=e%5E%28-%28C%29%2A%28p%2Bq%29%29%29
ln%28q%2Fp%29=-C%2A%28p%2Bq%29
C=-ln%28q%2Fp%29%2F%28p%2Bq%29
C=ln%28p%2Fq%29%2F%28p%2Bq%29
highlight%28C=%28ln%28p%29-ln%28q%29%29%2F%28p%2Bq%29%29