Question

A bacteria population has been decreasing exponentially. Twenty hours ago the
population was 1 million. Ten hours ago the population had decreased to half a million. If
the population keeps decreasing in this same pattern, how big was this bacteria
population one hour ago?

Answer 1

Answer:

  268,000

Step-by-step explanation:

You want to know the population of bacteria an hour ago if it was 1 million 20 hours ago and 1/2 million 10 hours ago, and decreasing exponentially.

Exponential function

The population can be described by a function of the form ...

  P = p0·(1/2)^(t/h)

where p0 is the initial population, and h is the half-life.

Application

Here, we have p0 = 1 million, h = 10 hours, and we want to evaluate this function at t=19.

The population is ...

  P = 1·(1/2)^(19/10) ≈ 0.2679 . . . . million

The population an hour ago was about 268 thousand.

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Additional comment

The population figures are given to 1 significant figure, so we cannot legitimately report population down to the units. Even the number 268,000 probably has more precision than is justified.