The mathematical model for learning an assembly-line procedure needed for assembling one component of a manufactured item is n = -5 In (0.89/P-1)

Question

The mathematical model for learning an assembly-line procedure needed for assembling one component of a manufactured item is n = -5 In (0.89/P-1) where P is the proportion of correctly assembled components after n practice sessions. Solve the equation for P to find an equation for the proportion of correctly assembled components in terms of the number of practice sessions n.

MULTIPLE CHOICE

a. P = 0.89 • (e^n/5 +1)

b. P = 0.89/(e^-5n+1)

c. P = 0.89/(e ^-n/5+1)

d. P = 0.89/(e ^-5/n+1)

e. P = 0.89/(e ^n/5+1)

Use the model to predict the percent of components that will be correctly assembled after 6 practice sessions.

If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth of a percent, if needed.

The percent of correctly assembled components is  ?  %

Answer 1

n = -5ln(0.89/P - 1)

n/-5 = ln(0.89/P - 1)

e^n/-5 = e^{ln(0.89/P - 1)}

e^n/-5 = 0.89/P - 1

e^n/-5 + 1 = 0.89/P

Pe^n/-5 + 1 = 0.89

P = 0.89/(e^-n/5 + 1)

C

Answer 2

n = -5ln(.89/(P-1))

-n/5 = ln(.89/(P-1))

e^-n/5 = .89/(P-1). Take reciprocal of each side.

e^n/5 = (P-1)/.89

P = .89e^n/5 + 1. (This doesn't correspond to any of the given answer choices?)

P(6) ~ 3.955