QuestionMay 25, 2025

13. A scientist puts a sample of 4000 bacteria in a Petri dish The number of bacteria decreases at a rate of 2% per hour. Write an equation to represent the number of bacteria, b, as a function of time measured in hours, t. b(t)=4000(2)^t b(t)=4000+0.98t b(t)=4000+2t b(t)=4000(0.98)^t

13. A scientist puts a sample of 4000 bacteria in a Petri dish The number of bacteria decreases at a rate of 2% per hour. Write an equation to represent the number of bacteria, b, as a function of time measured in hours, t. b(t)=4000(2)^t b(t)=4000+0.98t b(t)=4000+2t b(t)=4000(0.98)^t
13. A scientist puts a sample of 4000 bacteria in a Petri dish The number of bacteria decreases at a rate of 2% per hour. Write an equation to represent the number of bacteria, b, as a function of time measured in hours, t. b(t)=4000(2)^t b(t)=4000+0.98t b(t)=4000+2t b(t)=4000(0.98)^t

Solution
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Answer

b(t) = 4000(0.98)^t Explanation 1. Identify the decay rate The bacteria decrease at a rate of 2\% per hour, which means they retain 98\% of their number each hour. This is represented as 0.98. 2. Write the exponential decay function The general formula for exponential decay is **b(t) = b_0 \cdot (1 - r)^t**, where b_0 is the initial amount and r is the decay rate. Here, b_0 = 4000 and r = 0.02, so the equation becomes b(t) = 4000 \cdot (0.98)^t.

Explanation

1. Identify the decay rate<br /> The bacteria decrease at a rate of $2\%$ per hour, which means they retain $98\%$ of their number each hour. This is represented as $0.98$.<br /><br />2. Write the exponential decay function<br /> The general formula for exponential decay is **$b(t) = b_0 \cdot (1 - r)^t$**, where $b_0$ is the initial amount and $r$ is the decay rate. Here, $b_0 = 4000$ and $r = 0.02$, so the equation becomes $b(t) = 4000 \cdot (0.98)^t$.
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