A culture of bacteria has an initial population of 39000 bacteria and doubles every 9 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 2 hours, to the nearest whole number?

10077

Step-by-step explanation:

A culture of bacteria has an initial population of 5400 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 9 hours, to the nearest whole number?

P_0=5400

P

0

=5400

The initial population

t=9

t=9

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=5400\cdot 2^\frac{9}{10}

P

t

=5400⋅2

10

9

Plug in

P_t=10076.7563\approx10077

P

t

=10076.7563≈10077

Use parenthesis in the calculator for the exponent

step-by-step explanation:

graph using a few selected

x         y

-1       15

0         6

1         2.4

2       0.96

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