The first unit took 10 hours and the fourth unit 8.1 hours. What is the improvement rate?

A) 99%
B) 95%
C) 90%
D) 15%
E) none of the above

Question

The first unit took 10 hours and the fourth unit 8.1 hours. What is the improvement rate?A)  99%B)  95%C)  90%D)  15%E)  none of the above

Jarin Hasan · Accepted Answer

Final Answer : E, Explanation :   The improvement rate can be calculated using the formula for learning curve or improvement rate:   R = ( T n T 1 ) 1 n − 1 R = \left(\frac{T_n}{T_1}\right)^{\frac{1}{n-1}} R = ( T 1 ​ T n ​ ​ ) n − 1 1 ​  , where   T n T_n T n ​   is the time taken for the nth unit,   T 1 T_1 T 1 ​   is the time taken for the first unit, and   n n n   is the unit number. For the fourth unit (  n = 4 n=4 n = 4  ),   T 1 = 10 T_1=10 T 1 ​ = 10   hours and   T 4 = 8.1 T_4=8.1 T 4 ​ = 8.1   hours, the formula becomes   R = ( 8.1 10 ) 1 4 − 1 = ( 0.81 ) 1 3 R = \left(\frac{8.1}{10}\right)^{\frac{1}{4-1}} = \left(0.81\right)^{\frac{1}{3}} R = ( 10 8.1 ​ ) 4 − 1 1 ​ = ( 0.81 ) 3 1 ​  . This does not match any of the given options directly, indicating the correct answer is E, none of the above. To find the exact improvement rate, you would calculate the third root of 0.81, which is approximately 0.93 or 93%, not listed among the options.

The first unit took 10 hours and the fourth unit 8.1 hours. What is the improvement rate?

A) 99%
B) 95%
C) 90%
D) 15%
E) none of the above

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