Question

An antibiotic kills 60% of bacteria in a sample of 100,000 each day. The equation p₁ = 100,000(0.4)ᵈ represents 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 p₂ = 100,000(0.4)⁽ᵈ⁻⁴⁾. Which equation is equivalent to p₂?

a) p₂ = 100,000(0.4)ᵈ
b) p₂ = 100,000(0.4)ᵈ⁻⁴
c) p₂ = 100,000(0.4)⁽ᵈ⁻⁴⁾
d) p₂ = 100,000(0.4)⁽ᵈ⁺⁴⁾

Answer 1

The equivalent equation to p₂ = 100,000(0.4)⁽ᵈ⁻⁴⁾ for the second population of bacteria is option c) p₂ = 100,000(0.4)⁽ᵈ⁻⁴⁾.

Step-by-step explanation:

The equation that is equivalent to p2 = 100,000(0.4)(d-4) is c) p2 = 100,000(0.4)(d-4).

This equation represents the population of bacteria in a second sample, four days after an antibiotic has been introduced to a first sample with an initial population of 100,000 bacteria. The antibiotic kills 60% of the bacteria each day, so the population decreases to 40% of its size each day. The exponential growth equation p1 = 100,000(0.4)d represents the first sample, and the second sample, starting four days later, has to account for the four-day delay in the start of the antibiotic, reflected by the expression (d-4).