Question

Susan Sherer, an IRS auditor, took 45 minutes to process her first tax return. The IRS uses an 85% learning curve. The amount of processing time that Susan is going to require for the:

a) 2 nd Return___ minutes (round your response to two decimal places).
b) 4th Return ______ minutes (round your response to two decimal places).

Answer 1

The learning curve model predicts a decrease in task time with repetition due to efficiency gains. Susan Sherer will need approximately 38.25 minutes for the second tax return and about 32.51 minutes for the fourth return, applying an 85% learning curve.

Step-by-step explanation:

The question is related to the concept of the learning curve, which is a mathematical model that represents how the time to perform a task decreases with repetition due to learning and increased efficiency. Specifically, the task in question is processing IRS tax returns. An 85% learning curve implies that each time the number of tax returns processed doubles, the time taken to process each return will be reduced to 85% of the previous time.

For the second tax return, Susan is expected to take 85% of the time she took for the first return. Since the first return took 45 minutes:

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• a) 2nd Return = 45 minutes × 85% = 45 minutes × 0.85 = 38.25 minutes

For the fourth return, we apply the learning curve again, as it is another doubling. So, the fourth return will take 85% of the time of the second:

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• b) 4th Return = 38.25 minutes × 85% = 38.25 minutes × 0.85 ≈ 32.51 minutes

It is important to note that the learning curve is applicable only when the task is sufficiently repetitive and there are opportunities for efficiency gains through learning.

Answer 2

The learning curve implies that with each doubling of tasks done, the time required is reduced to 85% of the previous time. Using this 85% learning curve, the time Susan Sherer will require for the 2nd tax return would be 38.25 minutes, and for the 4th tax return, it would be 32.54 minutes, both rounded to two decimal places.

Step-by-step explanation:

The question pertains to the application of a learning curve and how it affects the time required to complete tasks with repeated experience. A learning curve is a graphical representation that shows the improvement in performance (e.g., time taken to complete a task) with experience. The IRS uses an 85% learning curve, which means that for every doubling of the cumulative quantity of units produced (or tasks completed), the unit time will decrease to 85% of the previous unit's time.

To calculate the time that Susan Sherer, an IRS auditor, is going to require for the 2nd tax return, we apply the 85% learning rate to the initial time of 45 minutes:

T(n) = T(1)×n(log base 2 of 0.85)

For the 2nd return, where n=2:

T(2) = 45×(2(log base 2 of 0.85))
= 45×(2-0.2345)

Performing the calculation:

T(2) = 45×(0.85)

T(2) = 38.25 minutes (rounded to two decimal places)

Similarly, for the 4th tax return, where n=4:

T(4) = 45×(4(log base 2 of 0.85))

T(4) = 45×(0.85)

T(4) = 32.54 minutes (rounded to two decimal places)