Question

A culture of bacteria has an initial population of 870 bacteria and doubles every 3 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 7 hours, to the nearest whole number?

Answer 1

The population of bacteria in the culture after 7 hours can be calculated using the formula Pt = P0 ⋅ 2t/d. Given an initial population of 870 bacteria and a doubling time of 3 hours, the population after 7 hours is approximately 3,120.

Step-by-step explanation:

The population of bacteria in the culture after 7 hours, to the nearest whole number, can be calculated using the formula Pt = P0 ⋅ 2t/d.

In this formula, Pt represents the population after t hours, P0 is the initial population, t is the time in hours, and d is the doubling time.

Given that the initial population is 870 bacteria and the doubling time is 3 hours, we can substitute these values into the formula:

Pt = 870 ⋅ 27/3

Using a calculator, we can evaluate this expression to find that the population of bacteria in the culture after 7 hours is approximately 3,120.