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Math Invitational for Girls
2019 MIG
22
22
Part of
2019 MIG
Problems
(1)
2019 Individual #22
Source:
5/1/2022
Scientists perform an experiment on a colony of bacteria with an initial population of
32
32
32
. The scientists expose the bacteria to alternating rounds of light and darkness. They first put the bacteria in a bright environment for one hour before placing it in a dark room for the second hour, and then repeating this process. Because they are vulnerable to light, the population of the bacteria will be halved in one hour of exposure to sunlight. However, in one hour of darkness, the population triples. How many hours will it take for the bacteria’s population to exceed
150
150
150
?
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<span class='latex-bold'>(A) </span>\text{between }4\text{ and }5\qquad<span class='latex-bold'>(B) </span>\text{between }5\text{ and }6\qquad<span class='latex-bold'>(C) </span>\text{between }6\text{ and }7\qquad<span class='latex-bold'>(D) </span>\text{between }7\text{ and }8\qquad<span class='latex-bold'>(E) </span>\text{between }8\text{ and }9
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2019 Individual