A culture of bacteria has an initial population of 460 bacteria and doubles every 4 hours. Using the formula [tex]P_t = P_0 \cdot 2^{t/d}[/tex], where [tex]P_t[/tex] is the population after [tex]t[/tex] hours, [tex]P_0[/tex] is the initial population, [tex]t[/tex] is the time in hours, and [tex]d[/tex] is the doubling time, what is the population of bacteria in the culture after 11 hours, to the nearest whole number?

Using the exponential growth formula with the initial population of bacteria at 460 and a doubling rate of every 4 hours, the population after 11 hours is calculated to be approximately 5484 bacteria when rounded to the nearest whole number.

Explanation:

To calculate the population of bacteria in the culture after 11 hours, we will use the provided formula Pt = P0 2t/d, where Pt is the final population, P0 is the initial population, t is the time in hours, and d is the doubling time in hours. In this case, the initial population P0 is 460 bacteria, the time t is 11 hours, and the doubling time d is 4 hours.

Substituting the given values into the formula:

Pt = 460 * 211/4

To find 211/4, we divide 11 by 4, which is 2.75, and then raise 2 to the power of 2.75. After calculating this, we get approximately 11.92. Multiplying this by the initial population:

Pt = 460* 11.92

=approx 5484.32

Rounded to the nearest whole number, the population of bacteria after 11 hours is approximately 5484 bacteria.