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A culture of bacteria has an initial population of 12000 bacteria and doubles every 6 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 t hours, P_0P 0 ​ is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 17 hours, to the nearest whole number?

User Priti
by
5.9k points

2 Answers

2 votes

Answer:Pt 85526.2769 = 85526

Explanation:

User Kayser
by
6.6k points
2 votes

Answer:

85,524 bacteria

Explanation:

Given the population of bacteria modelled by the equation where;


P_t = P_0\cdot 2^{(t)/(d)

P0 is the initial population

t is the time in hours

d is the doubling time

If the culture of bacteria has an initial population of 12000 bacteria, this means that;

at t = 0, P0 = 12000

substitute into the modelled function


P_t = P_0\cdot 2^{(t)/(d)\\\\P_t = 12000\cdot 2^{(0)/(d)\\\\\\P_t =12000\cdot 2^(0)\\\\P_t = 12000

If the population doubles every 6 hours

at t = 6, Pt = 24000


P_t = P_0\cdot 2^{(t)/(d)\\\\\\24000 = 12000\cdot 2^{(6)/(d)\\\\\\\\24000/12000 = 2^{(6)/(d)\\\\\\\\


2 = 2^{(6)/(d) }\\1 = 6/d\\d = 6\\

Next is to get the population of bacteria in the culture after 17 hours

at t = 17, Pt = ?


P_t = P_0\cdot 2^{(t)/(d)\\\\P_t = 12000\cdot 2^{(17)/(6)\\\\\\\\P_t = 12000\cdot 2^( 2.833 )\\P_t = 12000\cdot 2^( 2.833 )\\P_t = 12000 * 7.127\\P_t = 85,524.3

Hence the population of bacteria in the culture after 17 hours, to the nearest whole number is 85,524 bacteria

User Speck
by
6.4k points
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