Question 259316
I am not familiar with this formula. I am going to assume that it is
{{{t = (1/c)(ln(A) - ln(A-N))}}}
If this is not correct, then perhaps what follow will help you figure the correct solution. If not, then repost your question and put parentheses around each numerator and denominator.<br>
a) Combining the two logarithms is simple if you know the appropriate property of logarithms: {{{log(a, (p)) - log(a, (q)) = log(a, (p/q))}}}. Using this on your formula we get:
{{{t = (1/c)(ln(A/(A-N)))}}}<br>
b) The solution to this part is to use the formula. You are told that the maximum  task is to master 65 signs, This is our value for A. The goal is for the chimpanzee is to learn 30 signs. This is our value for N. And you are told that the value for c for a chimpanzee is 0.03. Substituting these values into the formula we get:
{{{t = 1/(0.03)(ln(65/(65-30)))}}}
Simplifying this we get:
{{{t = 1/(0.03)(ln(65/35))}}}
{{{t = 1/(0.03)(ln(1.8571428571428571))}}}
{{{t = 1/(0.03)(0.6190392084062234)}}}
{{{t = 33.3333333333333333(0.6190392084062234)}}}
{{{t = 20.6346402802074467}}}
(You are welcome to round these numbers off as desired.) From the formula and the information we were given, it will take a chimpanzee nearly 21 weeks to master 30 of the 65 signs.