Answer :
Using the formula [tex]\(P_t = P_0 \times 2^{\frac{t}{d}}\)[/tex], with an initial population[tex]\(P_0 = 65000\)[/tex]and a doubling time of[tex]\(d = 2\)[/tex] hours, after 13 hours, the bacteria population reaches approximately 8,320,000.
To calculate the population of bacteria after 13 hours using the formula [tex]\(P_t = P_0 \times 2^{\frac{t}{d}}\),[/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.
[tex]\(d\)[/tex] is the doubling time.
Given:
[tex]\(P_0 = 65000\)[/tex] (initial population)
[tex]\(d = 2\)[/tex] (doubling time)
[tex]\(t = 13\)[/tex] hours
Substitute these values into the formula:
[tex]\[ P_{13} = 65000 \times 2^{\frac{13}{2}} \][/tex]
Let's calculate the exponent first:
[tex]\[ 2^{\frac{13}{2}} = 2^6.5 \][/tex]
Now, calculate the result:
[tex]\[ 2^6.5 \approx 128 \][/tex]
Substitute the calculated value back into the equation:
[tex]\[ P_{13} = 65000 \times 128 \][/tex]
[tex]\[ P_{13} = 8,320,000 \][/tex]
Therefore, after 13 hours, the population of bacteria in the culture, to the nearest whole number, is approximately 8,320,000.
complete the question
A culture of bacteria has an initial population of 65000 bacteria and doubles every 2 hours. Using the formula Pt = Po 2a, where Pt is the population after t hours, Po 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?