Hawkins Products,Inc.,has found that new products follow a learning curve.The first two units have been completed with the following results: How much time will be needed to complete the 4^th unit? A)74.00 hours B)57.80 hours C)56.00 hours D)54.40 hours

Question

Quizplus · Accepted Answer

Using the learning curve formula, we can solve for k.

(2 units) = a * (1^k - 1)
(8 units) = a * (3^k - 1)

Dividing the second equation by the first:
4 = 3^k
k = log base 3 of 4 ≈ 0.631

Now we can use the learning curve equation to solve for the time needed for the 8th unit.

y = a * x^k
y = a * (8^0.631)
y = a * 3.998

To find a, we can plug in the values from the first two units:
23.40 = a * (1^0.631)
74.60 = a * (2^0.631)

Solving this system of equations gives us: 
a = 26.63

Now we can find the time for the 8th unit:
y = 26.63 * (8^0.631)
y ≈ 57.80 hours