calculating exponential distributions for products going bad

Question

half of our products (follows an exponential distribution) gone bad during a a week. calculate how long does it take for 1/3 of the products to go bad?

my answer (I put this in calculator and get no results):

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the correct answer is suppose to be 1.6 weeks

Half of the products going bad during one week. How can it be, that it needs 1.6 weeks that only 1/3 of the products going bad ? — callculus42, Oct 12 '14 at 16:59
Do you have another result, which fits to the exercise ? Is there a typo somewhere ? — callculus42, Oct 12 '14 at 17:48

score 0 · Accepted Answer · answered Oct 12 '14 at 23:39

I would say, that the decrease of the good products is exponential. Every week the good products decrease about 50%. Thus the equation is:

$y(t)=0.5^t$

y(t)=Proportion of good products to to all products.

t=weeks since the beginning of deterioration.

Having 2/3 bad products is the same as having 1/3 of good products.

$\frac{1}{3}=0.5^t$

This equation has to solved for t.

After approximate 1.6 weeks you will have 2/3 of bad products. Not 1/3 as in the given solution.

calculating exponential distributions for products going bad

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