Scientists are growing bacteria in a culture. At the beginning of each day, the scientists use a microscope to count the number of bacteria present. On day 1, there are 18 bacteria present. Based on their counts, they determine that the number of bacteria increase at a rate of 20% per day. During which day will the daily count first exceed 100 bacteria?a. 3 b.4 c.10 d.11

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ayeitsmariam ayeitsmariam · Answer 1 · 2020-09-18T04:58:15+02:00

Answer:11

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jainveenamrata jainveenamrata · Answer 2 · 2022-07-15T08:49:17+02:00

The number of the day that counted first exceed 100 bacteria will be 10. Then the correct option is C.

Consider the function:

y = a (1 ± r) ˣ

Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.

Scientists are growing bacteria in a culture.

At the beginning of each day, the scientists use a microscope to count the number of bacteria present.

On day 1, there are 18 bacteria present.

Based on their counts.

Then the number of bacteria increase at a rate of 20% per day will be.

Then the equation will be

y = 18 (1 + 0.2)ˣ

y = 18(1.2)ˣ

Then the number of the day that counted first exceed 100 bacteria will be

100 = 18(1.2)ˣ

5.556 = 1.2ˣ

Taking log, then we have

log 5.56 = x log 1.2

x = 9.405 ≈ 10

Then the correct option is C.

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