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Sagot :
It will take 5.83 hours for the bacteria to reach 1119.
What is exponential Growth ?
Exponential growth is when the quantity increases according to the function
[tex]P_t = P_0 e^{ kt}[/tex]
It is given in the question that
Initial number of Bacteria is 50
After 3 hours the bacteria has increased to 80
The bacterial growth is an exponential growth
[tex]P_t = P_0 e^{ kt}[/tex]
[tex]80 = 50 e^{ k * 3}[/tex]
Applying log on both sides
1.6 = 3*k
k = 1.6/3
k = 0.533
if this rate of growth continues, how much more time will it take for the number of bacteria to reach 1119
[tex]1119 = 50e^{0.533* t}\\\\3.18 = 0.533 *t\\\\5.83 = t[/tex]
Therefore it will take 5.83 hours for the bacteria to reach 1119.
To know more about exponential growth.
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Answer:
16.8 hours
Step-by-step explanation:
An exponential population increase can be modeled by the function ...
p(t) = a·b^(t/p)
where 'a' is the initial value (at t=0), b is the multiplier in time period p.
__
setup
The colony increased by a factor of b = 80/50 = 1.6 in p = 3 hours. Since we want to find the additional time to reach a population of 1119, the initial population we're working with is 80, not 50.
p(t) = 80·1.6^(t/3)
1119 = 80·1.6^(t/3)
__
solution
Solving this for t, we find ...
1119/80 = 1.6^(t/3) . . . . . . . . . . . . divide by 80
log(1119/80) = (t/3)log(1.6) . . . . . take logarithms
t = 3·log(1119/80)/log(1.6) . . . . . divide by the coefficient of t
t ≈ 16.8 . . . . hours
It will take about 16.8 more hours for the population to increase from 80 to 1119.
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