The first unit took 10 hours and the eighth unit took 1.25 hours. what is the learning curve

Learning curve basics:Assumption: Learning curve rate, r<=1
Relation: T_2k=r*T_kwhich implies T_N=(initial time)*N^bwhere b=log(r)/log(2).
Question:
The first unit took 10 hours and the eighth unit took 1.25 hours. what is the learning curve
Solution:Here(initial time)=T_1=10N=8, T_8=1.25
Method 1:using T_2k=r*T_kT_1=10, T_2=10r, T_4=10r^2, T_8=1.25=10r^3=>1.25=10r^3r=(1.25/10)^(1/3)=0.5
Method 2:using T_N=(T_1)*N^b, b=log(r)/log(2)T_8=1.25=10*8^(log(r)/log(2))use log_21.25=10*8^(log_2(r)/log_2(2))1.25/10=8^(log_2(r))           [ log_2(2)=1 ]switch sides and take log_2log_2(r)log_2(8)=log_2(1/8)3log_2(r)=-3     [log_2(8)=3, log_2(1/8)=-3]log_2(r)=-1r=2^(-1)=1/2^1=1/2
Answer using either method, learning curve rate is 1/2

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