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A culture of bacteria has an initial population of 65,000 bacteria and doubles every 2 hours. Using the formula [tex]P_t = P_o \cdot 2^{\frac{t}{d}}[/tex], where [tex]P_t[/tex] is the population after [tex]t[/tex] hours, [tex]P_o[/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 13 hours, to the nearest whole number?

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?

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