There are 70,000 bacteria present in a culture. an antibiotic is introduced to the culture and the number of bacteria is reduced by half every 4 hours. which of the following statements are true? select all that apply

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.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

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step-by-step explanation: