The first unit of a product took 832 hours to build, and the learning curve is 75%. How long will it take to make the 10th unit? (Use at least three decimals in the exponent if you use the logarithmic approach.)
A) less than 250 hours
B) from 251 to 275 hours
C) from 276 to 300 hours
D) from 301 to 325 hours
E) 325 or more hours

Question

Quizplus · Accepted Answer

We can use the learning curve formula to find out how long it will take to build the 10th unit.

Learning curve formula: Y = aX^b

Y = time to produce the 10th unit
a = time to produce the first unit
X = 10 (number of units)
b = log(learning rate)/log(2)

Note: We use log base 2 because the learning rate is given as a percentage and the formula requires it to be in a decimal form.

Plug in the values:

Y = 832 * 10^b
b = log(75%)/log(2) = -0.415 (rounded to three decimals)

Y = 832 * 10^(-0.415)
Y ≈ 305 hours

Therefore, it will take from 301 to 325 hours to produce the 10th unit.

The best choice is D, from 301 to 325 hours.

The First Unit of a Product Took 832 Hours to Build