11
AssignmentMultiple Choice

Exponential and Logarithmic Inequalities

Question 11 • CUSD Advanced Math A (5.0)

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?

Answer
A
3
B
4
C
10
D
11

Explanation

The count on day n is 18 × 1.2^(n−1), since it starts at 18 and grows by 20% each day. On day 10, the count is about 18 × 1.2^9 = 93, which is still below 100. On day 11, it is about 18 × 1.2^10 = 111, so the count first exceeds 100 on day 11.

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