I need assistance with the following question Formula t1cln

I need assistance with the following question:

Formula t=1/c[ln A-ln(A-N)] describes the time, t, in weeks, that 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 go be achieved, and c is a constant used to measure an indiviuals learning style.

a. Express the formula so that the expression in brackets is written as a single logarithm.

b. Use the form of the formula from part a to answer this question. An animal learning sign language can master a maximum of 120 signs. How many weeks will it take the animal master 64 signs if the constant c for that animal is .04?

I have the expression with the quotient rule:

t=1/.04 ln(120/64) then = 1/.04 ln(120/120-64)

t=1/.04 ln(120/56)

the answer came out to be 20 weeks, however i do not understand how to put the 1/.04 into the equation after i determine t=1/.04 ln(120/56)

any assistance would be greatly appreciated

Solution

t = (1/c{ lnA/(A-N)}

A = 120 ;N = 64 ; c= 0.04

t = (1/0.04)ln(120/56)

use calculator to find (ln(120/56) = 0.762

t = (1/0.04)*0.0762 = 0.762/0.04 = 19.05 weeks