Discussion Frum Unit 5

The population of a culture of bacteria is modeled by the logistic equation

P (t) = 14250

1 + 29e-0.62t

To the nearest tenth, how many days will it take the culture to reach 75% of its carrying capacity?

D1A

75 x 14250 = 10,687.50
100
10,687.50 = 14250
1 + 29e-0.62t

10,687.50 = 14250
1 + 29e-0.62t t∈

10,687.50 (1 + 29e-0.62t) = 14250
10,687.50 + 309937.5e-0.62t = 14250
309937.5e-0.62t = 14250 - 10,687.50
309937.5e-0.62t = 3562.50
-0.62t
e =1
87

-06.62t = -ln (87)

t = ln (87) x 50
31

t ≈ 7. 20308

It will take 7.2 days for the culture to reach 75% of carrying capacity.




What is the carrying capacity?

The logistic growth model is approximately exponential at first, but it has a reduced rate of growth as the

output approaches the model’s upper bound, called the carrying capacity (Abramson, 2017, p. 544).

Carrying capacity in a logistic model, the limiting value of the output (Abramson, 2017, p. 565). In logistic

development, a population's per capita development rate gets littler and littler as populace size approaches

a maximum forced by constrained assets within the environment, known as the carrying capacity (K).