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Hi Cath.
Please advise on the below.
111 A company has recently launched a new product.
The average time taken for the first 4 units was 24 minutes per unit and the average time taken for the first 32 units was 9.34 minutes per unit.Calculate the rate of learning that occurred to the nearest %.
Solution:
to go from 4 units to 32 you would have to double 3 times.
therefore 32r^3=9.34
r^3=0.291875 this tells me the average time per unit for the first 32 units.
we then divide 0.291875 by 24 minutes
r^3=0.01216
this tells us 1.2% of the time taken to produce the first unit? or is this the time taken to produce the 4th unit?r=22.9%
which is the wrong answer.
I am use to seeing questions where we have the time for the first unit.. could you help me understand where I have gone wrong here.
Hi there… you are nearly there…. being asked to find the rate of learning is one of the commonly asked learning curve questions so it is excellent that you are flagging this up if you don’t follow. Its only ever asked with relatively small units of numbers and this is because the method to solve it doesn’t really fit with the other learning curve type exercises where you use the formula.
Ok
So you know the learning curve rule says that as cumulative output doubles ( 1 to 2 to 4 to 8 to 16 to 32) the cumulative average time taken per unit decreases by a constant percent. The learning rate is that constant percent.
So as you stated correctly to jump from 4 units to 32unit you need to double output 3 times – i.e. 3 jumps.
The average time per unit when you reach 4 units is given – this is 24mins per unit. This figure is the cumulative average.
The average time per unit when you reach 32 units is 9.34 mins per unit.So we need to find what number (call ‘n’) that when multiplied three times will turn 24 into 9.34.
Stated in equation form:
24 * n * n * n = 9.34
which can also be written as: 24 * n^3 = 9.34
By rearranging it we find n = 3?0.38916666 ( this requires the cubed root button on your calculator)
The answer comes out as approx 0.73 or 73% rate of learning.
If you check back this should work….
There is another example in Open Tuition CIMA P2 notes – exercise 5 pg 38/40. It doesn’t matter that you are given the time for the first item – when finding the learning rate – you don’t use the formula method – you only care about the number of jumps it takes to double the output.
thanks cath. I am not sure if my responses are being saved! but I will post again. Thanks. I will need to work through the example again and exercise 5. So will come back if I have questions.
thanks
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