Expert: Jack Cheng - 11/28/2006

Question
Durring an economic recession, the number (N) of active stock market traders at time (t) after the recession started is found to decrease exponentially according to N=Noe^-t/10, where (t) is measured in months. The bank has decided to wait for the number of traders to havle from the initial value (No) before it cuts intrest rates. How many months will the bank wait, answer to be given in terms of natural log (LN)

Answer
Hi Mark,

Sorry about the delay; I was out for a while.

N = 1/2 N.    (I used N. instead of No because o looks like another variable)

1/2N. = N.e^(-t/10)
1/2   = e^(-t/10)
ln (1/2) = -t/10
      t = -10 ln (1/2)
      t = -10 (ln 1 - ln 2)
      t = -10 (-1 - ln 2)
      t = 10 + 10 ln 2

I used some properties of logarithm. Look them up if you don't recognize them.

I hope this helps.

Jack