Answer:
24 hours after the antibiotic is introduced, the number of bacteria in the culture is reduced to 1093; The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay; The function B(x) = 70000(0.5)ˣ, where x represents the number of 4 hour periods, represents the amount of bacteria present after the antibiotic is introduced.
Step-by-step explanation:
In any situation where an amount grows or declines by a set percent every time period can be represented using an exponential function. Since the amount of bacteria is reduced by half, or 50%, every 4 hours, this is exponential decay.
Exponential functions such as this are of the form
y = a(1+r)ˣ, where a represents the initial population, r is the percent of growth or decrease, and x is the number of time periods. In this situation, the initial population, a, is 70000. Since the number of bacteria decreases by half, r = -0.50. This gives us
y = 70000(1+-0.50)ˣ, or y = 70000(0.50)ˣ.
In 24 hours, there are 6 4-hour periods. This means x = 6; this gives us
y = 70000(0.50)⁶ = 1093.75.
