The management at a plastics factory has found that the maxi

The management at a plastics factory has found that the maximum number of units a worker can produce In a day is 40. The learning curve for the number N of units produced per day after a new employee has worked t days Is modeled by N = 40(1 - e^kt). After 20 days on the job, a new employee produces 18 units. Find the learning curve for this employee (first, find the value of k). k = N = How many days should pass before this employee Is producing 23 units per day? (Round your answer to the nearest whole number.) days

Solution

N = 40( 1- e^kt)

20 days ---- 18 units

plug this set of data to solve for k :

18 = 40(1-e^20k)

18/40 = 1-e^20k

e^20k = 0.55

taking natural log on both sided:

a) 20k = ln(0.55) ----> k =-0.030

N = 40( 1- e^-0.03t )

b) N = 23 find t=?

23 = 40 (1-e^-0.03t)

e^-0.03t = 0.425

taking natural log on both sides:

-0.03t = ln(0.425)

t = 28.52 = 29 days