Andrew M. answered • 02/01/18

Tutor

New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

If the can reduces its weight by 10% each month, then in any given

month the weight is 90% of the previous months.

Weight as a function of number of months is found by the equation:

W(m) = W

_{0}(0.9)^{m}If we start at 24 kg and we want to weigh "at least 6kg less than original weight"

we want w(m) ≤ 24-6 or w(m) ≤ 18 kg

24(0.9)

^{m}≤ 180.9

^{m}^{ }≤ 18/240.9

^{m }≤ 3/40.9

^{m }≤ 0.75We want the smallest number for m that will cause 0.9

^{m }≤ 0.75Since we don't want to use logarithms for an exact answer then let's

plug in a small number for m and compare the answer to 0.75

m=1: 0.9

^{1}= 0.9 not less than 0.75m=2: 0.9

^{2}= 0.81 not less than 0.75m=3: 0.9

^{3}= 0.729 YES this is less than 0.75Your answer is m = 3 months

Andrew M.

02/01/18