Question

A culture of bacteria has an initial population of 8300 bacteria and doubles every 10 hours. Using the formula Pt=P0*2^t/d , where Pt is the population after t hours, P0 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 3 hours, to the nearest whole number?

Answer 1

10218

Explanation:

A culture of bacteria has an initial population of 8300 bacteria and doubles every 10 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P

t

​

=P

0

​

⋅2

d

t

​

, where P_tP

t

​

is the population after t hours, P_0P

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 3 hours, to the nearest whole number?

P_0=8300

P

0

​

=8300

The initial population

t=3

t=3

Time elapsed

d=10

d=10

The doubling time

P_t = P_0\cdot 2^{\frac{t}{d}}

P

t

​

=P

0

​

⋅2

d

t

​

P_t=8300\cdot 2^\frac{3}{10}

P

t

​

=8300⋅2

10

3

​

Plug in

P_t=10218.4986\approx10218

P

t

​

=10218.4986≈10218

Use parenthesis in the calculator for the exponent

10218

Answer 2

10,219 bacteria

Explanation:

In this question, we are asked to calculate the population of bacteria in a culture given the formula for the population increase.

From the question, we know the formula to use is

Pt=Po*2^t/d

From the parameters in the question, we identify that Pt is ?, Po is 8300 bacteria , t is 3 hours and d is 10 hours which is the doubling time. Inserting these figures we have;

Pt = 8300 * 2^(3/10)

Pt = 8300 * 2^0.3

Pt = 10,218.5

Pt = 10,219 bacteria to the nearest whole number