Question

At the beginning of an experiment, there are 500 grams of contaminants. Each hour, one fourth of the contaminants are filtered out. How many grams of contaminants remain after 4 hours?

Show all your work for full credit.

Round your answer to the nearest hundredth. Use ^ for exponents. x^2 = x2

Answer 1

158.20 g

Explanation:

You want to know the remaining grams of contaminants after 4 hours if an experiment started with 500 g, and 1/4 of the contaminants are removed each hour.

Exponential model

At the end of each hour, 3/4 of the contaminants remain. The decay in amount can be modeled by the exponential function ...

remaining = (initial amount)·(decay factor)^(number of periods)

Application

Here, the initial amount is 500 g, the decay factor in an hour is 3/4, and the number of hours is 4:

remaining = (500 g)·(3/4)^4 ≈ 158.20 g

About 158.20 grams of contaminants remain.

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Additional comment

The "decay factor" is (1 + decay rate). Here, the decay rate is -1/4 per hour, so the decay factor is (1 -1/4) = (3/4) per hour.