QuestionAugust 6, 2025

3. Using Continuous Decay (Euler's Number) A scientist models bacteria decay using N(t)=500e^-0.35t How many bacteria remain after 3 hours?

3. Using Continuous Decay (Euler's Number) A scientist models bacteria decay using N(t)=500e^-0.35t How many bacteria remain after 3 hours?
3. Using Continuous Decay (Euler's Number)
A scientist models bacteria decay using
N(t)=500e^-0.35t
How many bacteria remain after 3 hours?

Solution
4.3(282 votes)

Answer

Approximately 174 bacteria remain after 3 hours. Explanation 1. Substitute the time into the decay formula Use t = 3 in the formula N(t) = 500e^{-0.35t}. 2. Calculate the exponent Compute -0.35 \times 3 = -1.05. 3. Evaluate the exponential function Calculate e^{-1.05} using a calculator. 4. Multiply by initial quantity Multiply the result by 500 to find N(3).

Explanation

1. Substitute the time into the decay formula<br /> Use $t = 3$ in the formula $N(t) = 500e^{-0.35t}$.<br />2. Calculate the exponent<br /> Compute $-0.35 \times 3 = -1.05$.<br />3. Evaluate the exponential function<br /> Calculate $e^{-1.05}$ using a calculator.<br />4. Multiply by initial quantity<br /> Multiply the result by 500 to find $N(3)$.
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