Question

A bacteria population decreases by a factor of 1/2 every 4 hours. Explain why we could also say that the population decays by a factor of (1/2 )^1/4 every hour.

Answer 1

(1/2)^(t/4) = ((1/2)^(1/4))^t

Explanation:

If time t is given in hours, then the number of 4-hour time periods is t/4. If the half-life is 4 hours, the population multiplier is ...

(1/2)^(t/4)

Using the rules of exponents, that can be rearranged to ...

(1/2)^((1/4)·t) = ((1/2)^(1/4))^t

That is, the multiplier every hour is ...

(1/2)^(1/4)

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The relevant rule of exponents is ...

(a^b)^c = a^(bc)