9
QuizMultiple Choice

Unit Test — Unit test

Question 9 • TX-Precalculus A

A colony of bacteria has 10,000 bacteria and is growing exponentially. The inequality 10,000(4x) ≥ 320,000 represents the hours, x, for which the colony will have at least 320,000 bacteria.Which interval represents the hours when the colony will have at least 320,000 bacteria?

Answer
A
[2.5, ∞)
B
[3, ∞)
C
[32, ∞)
D
[0, 2.5]

Explanation

Divide both sides of 10,000(4^x) ≥ 320,000 by 10,000 to get 4^x ≥ 32. Since 4^2.5 = 32 and 4^x increases as x increases, the inequality holds for x ≥ 2.5. The interval [2.5, ∞) represents those hours.

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