Question

A culture of bacteria has an initial population of 860 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 hours, P_0P 0 ​ is the initial population, is the time in hours and is the doubling time, what is the population of bacteria in the culture after 4 hours, ?

Answer 1

1170

Step-by-step explanation:P_0=860

P

0

​

=860

The initial population

t=4

t=4

Time elapsed

d=9

d=9

The doubling time

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

P

t

​

=P

0

​

⋅2

d

t

​

P_t=860\cdot 2^\frac{4}{9}

P

t

​

=860⋅2

9

4

​

Plug in

P_t=1170.2794\approx1170

P

t

​

=1170.2794≈1170