thomisonariel12
contestada

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of
4.3% per hour. How many hours does it take for the size of the sample to double?

Respuesta :

wizard123
Exponential growth model is:
[tex]P = e^{rt}[/tex]

r = .043
P = 2, this is double if initial population is 1

[tex]2 = e^{.043t}[/tex]

Solve for t.
Take log of both sides
[tex]ln(2) = ln(e^{.043t}) = .043t \\ \\ t = \frac{ln(2)}{.043}[/tex]
MrRoyal

The population of the bacteria is modeled by an exponential function.

The population of the sample will double after 16.5 hours

An exponential function is represented as:

[tex]\mathbf{y=a(1 + r)^x}[/tex]

Where

  • r represents the growth rate (i.e. 4.3%).
  • x represents the number of hours.
  • y represents the current population.
  • a represents the initial population.

When the population doubles, we have:

y = 2a

So, the equation becomes:

[tex]\mathbf{2a=a(1 + 4.3\%)^x}[/tex]

Divide both sides by a

[tex]\mathbf{2=(1 + 4.3\%)^x}[/tex]

[tex]\mathbf{2=(1.043)^x}[/tex]

Take logarithm of both sides

[tex]\mathbf{log(2)=log(1.043)^x}[/tex]

Apply law of logarithm

[tex]\mathbf{log(2)=xlog(1.043)}[/tex]

Divide both sides by log(1.043)

[tex]\mathbf{x = \frac{log(2)}{log(1.043)}}[/tex]

Divide

[tex]\mathbf{x = 16.5}[/tex]

Hence, the population will double after 16.5 hours

Read more about exponential function at:

https://brainly.com/question/3127939

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