We have been given that a culture of bacteria has an initial population of 22,000 bacteria and doubles every 5 hours. Using the formula [tex]P(t) = P_0\cdot 2^{\frac{t}{d}}[/tex], where P(t) is the population after t hours, [tex]P_0[/tex] is the initial population, t is the time in hours and d is the doubling time.
We are asked to find the population of bacteria after 17 hours.
First of all, we will substitute our given values in doubling life formula as:
[tex]P(t) =22,000\cdot 2^{\frac{t}{5}}[/tex]
Now to find population of bacteria after 17 hours, we will substitute [tex]t=17[/tex] in our formula as:
[tex]P(117) =22,000\cdot 2^{\frac{17}{5}}[/tex]
[tex]P(117) =22,000\cdot 2^{3.4}[/tex]
[tex]P(117) =22,000\cdot (10.556063286183)[/tex]
[tex]P(17) =232233.392296026[/tex]
[tex]P(17)\approx 232,233[/tex]
Therefore, the bacteria population will be 232,233 after 17 hours.
