Answer:
- half-life: 33.75 minutes
- formula: G(t) = 176(1/2)^(t/33.75)
- G(32) ≈ 91.2 g
Explanation:
Given 176 grams of goo decays to 11 grams in 135 minutes, you want the half-life, a formula for the remaining amount, and the amount remaining after 32 minutes.
Formula
The formula for the decay can be written as ...
remaining = (initial amount)×(decay factor)^(t/period)
where "period" is the period that results in a remaining amount of ...
(initial amount)(decay factor)
Here, the initial amount is given as 176 grams. The decay factor will be (11/176) after a period of 135 minutes. This means our equation can be written as ...
G(t) = 176(11/176)^(t/135)
G(t) = 176(1/16)^(t/135) . . . . simplify the decay factor
G(t) = 176((1/2)^4)^(t/135) . . . . recognizing 16 = 2^4
G(t) = 176(1/2)^(t/33.75) . . . . . in terms of half-life
Half-life
The half-life is the period associated with a decay factor of 1/2. Here, we have found it to be 33.75 minutes
The half-life is 33.75 minutes.
Remaining
After 32 minutes, the amount remaining is ...
G(32) = 176(1/2)^(32/33.75) ≈ 91.22 . . . . grams
About 91.2 grams of goo will remain after 32 minutes.
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