Half-life question?

Question

If Grandma’s cookies have a half life of 2 hours and she bakes 3 dozen cookies, how many hours will pass until only two cookies remain uneaten? Round your answer to the nearest minute.

Is it 8 hours and 22 minutes?

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Answer 1 · 2018-01-18T20:25:06

#8#h#20#min

#y(t) = a*(1/2)^(0.5t)#

(where #t# is in hours)

e.g. #y(2) = (1/2)^1 * 36 = 1/2 * 36#

(this is the number after the first half-life.)

#3# dozen #= 36#

#a = 36#

if #y(t) = 2#:

#2 = a*(1/2)^(0.5t)#

#2 = 36*(1/2)^(0.5t)#

#(1/2)^(0.5t) = 1/18#

#0.5t = log_(1/2)(1/18)#

#0.5t = 4.17#

#t = 8.339..#

#t = 8.339#h #= 8#h #20#min

(this answer is very close to #8#h #22# min, so you may have rounded differently, but used the right method.)