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Over time, the number of organisms in a population increases exponentially. The table below shows the approximate number of organisms after y years.y yearsnumber of organisms, n155260367475The environment in which the organism lives can support at most 600 organisms. Assuming the trend continues, after how many years will the environment no longer be able to support the population?

Respuesta :

MrRoyal

The environment will no longer be able to support the population after 24 years

How to determine the number of years?

The proper representation of the table is given as:

y   1   2    3  4

n 55 60 67 75

An exponential function is represented as:

[tex]n = ab^y[/tex]

Where:

  • a represents the initial value
  • b represents the rate.

Next, we determine the function equation using a statistical calculator.

From the statistical calculator, we have:

a = 49.19 and b = 1.11

Substitute these values in [tex]n = ab^y[/tex].

So, we have:

[tex]n = 49.19 * 1.11^y[/tex]

From the question, the maximum is 600.

So, we have:

[tex]49.19 * 1.11^y = 600[/tex]

Divide both sides by 49.19

[tex]1.11^y = 12.20[/tex]

Take the logarithm of both sides

[tex]y\log(1.11) = \log(12.20)[/tex]

Divide both sides by log(1.11)

y = 23.97

Approximate

y = 24

Hence, the environment will no longer be able to support the population after 24 years

Read more about regression equations at:

https://brainly.com/question/25226042

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