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qwelly [4]
3 years ago
13

A culture of bacteria has an initial population of 22000 bacteria and doubles every 5 hours. Using the formula P t = P 0 ⋅ 2 t d

P t ​ =P 0 ​ ⋅2 d t ​ , where P t P t ​ is the population after t hours, P 0 P 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?
Mathematics
1 answer:
Bas_tet [7]3 years ago
7 0

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 P(t) = P_0\cdot 2^{\frac{t}{d}}, where P(t) ​ is the population after t hours, ​P_0 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:

P(t) =22,000\cdot 2^{\frac{t}{5}}

Now to find population of bacteria after 17 hours, we will substitute t=17 in our formula as:

P(117) =22,000\cdot 2^{\frac{17}{5}}

P(117) =22,000\cdot 2^{3.4}

P(117) =22,000\cdot (10.556063286183)

P(17) =232233.392296026

P(17)\approx 232,233

Therefore, the bacteria population will be 232,233 after 17 hours.

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Answer:

64. 6138

66. 8.078125

Step-by-step explanation:

Let's take it one number at a time.

For number 64:

6(2)^{1-1}=6

6(2)^{2-1}=12

6(2)^{3-1}=24

6(2)^{4-1}=48

6(2)^{5-1}=96

6(2)^{6-1}=192

6(2)^{7-1}=384

6(2)^{8-1}=768

6(2)^{9-1}=1536

6(2)^{10-1}=3072

Sum = 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072

Sum = 6138

For number 66:

12(-\frac{1}{2})^{0}=12

12(-\frac{1}{2})^{1}=-6

12(-\frac{1}{2})^{2}=3

12(-\frac{1}{2})^{3}=-1.5

12(-\frac{1}{2})^{4}=0.75

12(-\frac{1}{2})^{5}=-0.375

12(-\frac{1}{2})^{6}=0.1875

12(-\frac{1}{2})^{7}=-0.0078125

12(-\frac{1}{2})^{8}=0.046875

12(-\frac{1}{2})^{9}=-0.0234375

Sum = 12 + -6 + 3 + -1.5 + 0.75 + -0.375 + 0.1875 + -0.0078125 + 0.046875 + -0.0234375

or to make things simpler:

Sum = 12 - 6 + 3 - 1.5 + 0.75 - 0.375 + 0.1875 - 0.0078125 + 0.046875 - 0.0234375

Sum = 8.078125

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