Question

A population of bacteria is declining at an exponential rate of 5% per day under the impact of a new medical drug. Find the population of bacteria after 20 days if the initial population of bacteria was 3,800,000.

Answer 1

1,362,247

Explanation:

You want the bacteria population after 20 days if the initial population of 3,800,000 is declining at the rate of 5% per day.

Population function

The population of bacteria can be expressed by the exponential function ...

population = (initial population) × (decay factor)^(time)

where ...

decay factor = 1 - decay rate . . . . . . . in the period equal to 1 time unit

Application

For a decay rate of 5% per day, this means our bacteria population in 20 days will be ...

p = 3800000·(1 -0.05)^20 ≈ 1,362,247

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Additional comment

The initial population is given to 2 significant figures, so it makes a certain amount of sense to give the result to approximately that precision:

1.36 million or 1.4 million bacteria after 20 days

(Sometimes when the leading digit is 1, it is useful to have one more significant figure.)