The population of bacteria after 40 hours is 254
Step-by-step explanation:
Initial population of bacteria = 40
Growth rate: Doubles every 15 hours
The population function is given as:
[tex]P_t = P_0 * r^t[/tex]
Here
P0 is the initial population
r is the growth rate
and t is the time in hours
The growth rate will be: [tex]2^{\frac{t}{15}}[/tex]
Putting the values in the function
[tex]P_t = 40 * 2^{\frac{40}{15}}\\P_t = 40 * 2^{2.67}\\P_t = 40 * 6.34960...\\P_t = 253.98416...[/tex]
Rounding off to nearest whole number we get
P_t ≅254
Keywords: Population growth,, bacteria
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From the information, the population of the bacteria will be 254.
Based on the information given, the population function will be:
= P × 2r
where, P = initial population of the bacteria
= 40 × 6.349
= 253.98
= 254
Therefore, it can be deduced that the population of the bacteria after 4 hours will be 254.
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