Answered

The population of a town is estimated to increase by 15% per year.
The population today is 20 thousand. Create the function to
represent the situation and find out what the population will be ten
years from now.
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Answer :

mhanifa
  • [tex]P(t) = 20000 * 1.15^t[/tex]
  • 80911

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Use an exponential growth function. The formula for exponential growth is:

  • [tex]P(t)=P*(1+r)^t[/tex]

Where:

  • P(t) is the future population
  • P is the current or initial population
  • r is the growth rate in decimals
  • t is the time in years.

Given:

  • P = 2000
  • r = 15% = 0.15
  • t = 10 years

Substitute the given values:

  • [tex]P(t) = 20000 * (1 + 0.15)^t[/tex]
  • [tex]P(t) = 20000 * 1.15^t[/tex]

To find the population in ten years (t = 10), we substitute:

  • [tex]P(10) = 20000 * 1.15^{10}[/tex]

Calculating this:

  • [tex]P(10) = 20000 * 1.15^{10} = 20000 * 4.04555773571 = 80911[/tex]

Therefore, the population in ten years will be approximately 80911.

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