formulas in algebra

Question

The formula t= 1/c [In A- In (A-N)]describes the time, t, in weeks, that it takes to achieve mastery of a portion of a task, where A is the maximum learning possible, N is the portion of the learning that is to be achieved, and c is a constant used to measure an individual’s learning style.
a. Express the formula so that the expression in brackets is written as a single logarithm.


b. The formula is also used to determine how long it will take chimpanzees and apes to master a task. For example, a typical chimpanzee learning sign language can master a maximum of 65 signs. Use the form of the formula from part (a) to answer this question: How many weeks will it take a chimpanzee to master 30 signs if c for that chimp is 0.03?

Answer 1

t = ln(A/(A-N))/c

 

A must be > 0 and A-N must be > 0

 

t = ln(65/(65-30))/(0.03) and ln(65/(65-30))/(0.03) = 20.63464029 weeks (approx.)