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Researchers recorded that a certain bacteria population declined from 220,000 to 700 in 36 hours. At this rate of decay, how many bacteria will there be in 18 hours?

Respuesta :

Eduard22sly

The number of bacteria that will be remaining in 18 hours, given it declined from 220,000 to 700 in 36 hours is 110344

How do I determin the number of bacteria in 18 hours?

We'll begin by obtaining the rate of decay using a linear decay method as shown below:

  • Let the coordinates be: (0 , 220000) and (36 , 700)
  • x coordinate 1 (x₁) = 0
  • x coordinate 2 (x₂) = 36
  • y coordinate 1 (y₁) = 220000
  • y coordinate 2 (y₂) = 700
  • Decay constant (K) =?

K = (y₂ -y₁) / (x₂ - x₁)

K = (700 - 2220000) / (36 - 0)

K = -219300 / 36

K = -6092 per hour

Finally, we shall determine the number of bacteria that will remain in 18 hours. Details below:

  • Decay constant (K) = 6092 per hour
  • Total bacteria (N₀) = 220000
  • Time (t) = 18 hours
  • Number of bacteria remaining (N) =?

N = N₀ - Kt

N = 220000 - (6092 × 18)

N = 220000 - 109656

N = 110344

Thus, number of bacteria that will remain is 110344

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