Respuesta :
Answer:
The population of the bacteria after 40 hours is 254.
Step-by-step explanation:
The initial population is 40 and the population of bacteria doubles every 15 hours.
The population function is defined as
[tex]P(t)=P_0\cdot (b)^{t}[/tex]
Where P₀ is initial population, b is exponential growth rate.
Since the population of bacteria doubles every 15 hours, therefore the growth rate is
[tex]2^{\frac{1}{15}}[/tex]
[tex]P(t)=40\cdot (2)^{\frac{1}{15}t}[/tex]
[tex]P(t)=40\cdot (2)^{\frac{t}{15}}[/tex]
We have to find the population of the bacteria after 40 hours, so put [tex]t=40[/tex] in the above equation.
[tex]P(t)=40\cdot (2)^{\frac{40}{15}}[/tex]
[tex]P(t)=40\times 6.3496[/tex]
[tex]P(t)=253.9842[/tex]
[tex]P(t)\approx 254[/tex]
Therefore the population of the bacteria after 40 hours is 254.
The population of the bacteria after 40 hours will be 254 bacterias.
From the information that was given, we are informed that the population of bacteria doubles every 15 hours and that the population of bacteria is 40.
Therefore, the equation to solve the question will be:
= 40 × 2^40/15
= 40 × 2^2.67
= 254
Therefore, the population of the bacteria after 40 hours will be 254 bacterias.
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