Question

A culture of bacteria has an initial population of 65000 bacteria and doubles every 2 hours. using the formula p, start subscript, t, end subscript, equals, p, start subscript, 0, end subscript, dot, 2, start superscript, start fraction, t, divided by, d, end fraction, end superscriptp t ​ =p 0 ​ ⋅2 d t ​ , where p, start subscript, t, end subscriptp t ​ is the population after t hours, p, start subscript, 0, end subscriptp 0 ​ is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 13 hours, to the nearest whole number?

Answer 1

To calculate the bacterial population after 13 hours, use the exponential growth formula and plug in the values: initial population (65,000), time (13), and doubling interval (2 hours). After calculations, the population is approximately 5,883,150 bacteria.

Step-by-step explanation:

The student's question regards the population growth of bacteria, which is a concept in mathematics that applies to biology. Using the provided formula for exponential growth pt = p0 · 2t/d, where p0 is the initial population, t is the time in hours, d is the doubling time, and pt is the population after t hours, we can calculate the population of bacteria after 13 hours.

The initial population (p0) is 65,000 bacteria, and the doubling time (d) is 2 hours. To find the population after 13 hours (t), we use the formula with these values:

pt = 65,000 · 213/2

First, divide 13 hours by the doubling time of 2 hours:

13/2 = 6.5

The population doubles 6.5 times in 13 hours. We calculate the doubling factor:

26.5 ≈ 90.510

Next, multiply the initial population by this factor:

pt = 65,000 · 90.510 ≈ 5,883,150

Therefore, the population of bacteria after 13 hours is approximately 5,883,150, to the nearest whole number.