Question

An antibiotic kills 60% of bacteria in a sample of 100,000 each day. The equation mc009-1.jpgrepresents the population, p1, after d days. Four days after introducing the antibiotic to the first sample, a scientist introduces the same antibiotic to a second population, p2. The number of bacteria after d days in the second population is represented by the equation mc009-2.jpg. Which equation is equivalent to p2?
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Answer 1

If p1(d) = 100000(0.4)^d and the second population is introduced 4 days later, then its age at global day d is d − 4. So

p2(d) = 100000(0.4)^{d-4}.

This is equivalent to multiplying by (0.4)^{−4}:

p2(d) = 100000(0.4)^{d-4} = 100000(0.4)^{d}·(0.4)^{-4} = 3,906,250(0.4)^d, for d ≥ 4.