At the time an antibiotic is applied to a population of bacteria, the population is growing as defined by the function p(x) = 300(1.05)x, where x represents time, in hours. At the same time, the antibiotic reduces the population by 30% each hour. The effect of the antibiotic can be represented by the function a(p) = p(0.7)x.Which function represents a(p(x))?
Substitute p(x) = 300(1.05)^x into the antibiotic function: a(p(x)) = 300(1.05)^x(0.7)^x. Since the exponents are both x, multiply the bases: 1.05 × 0.7 = 0.735. Thus the combined function is 300(0.735)^x, which is choice A.
AI-written and checked against the verified answer.