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A town’s population increases at a constant rate. In 2010 the population was 56,000. By 2012 the population had increased to 81,000. If this trend continues, predict the population in 2016.

Respuesta :

abidemiokin

The approximate population in 2016 is 91, 604 population

  • Let the time taken by the population to increase be "t"
  • Let the number of the population be P

The exponential equation representing the statement is [tex]P=P_0e^t[/tex]

  • If in 2010 the population was 56,000, then at t = 0, P0 = 56000

Substituting into the formula will give:

  • P = 56000

If by 2012 the population had increased to 81,000, then:

81000 =  56000e^12k

81000/56000 = e^12k

1.4464 = e^12k

ln1.4464 = 12k

0.3691 = 12k

k = 0.3690/12

k = 0.03076

Get the prediction of the population in 2016.

[tex]P = 56000e^{16(0.03076)}\\P=56000e^{0.49213}\\P = 56000(1.6357)\\P = 91,603.70[/tex]

Hence the approximate population in 2016 is 91, 604 population

Learn more on exponential function here:https://brainly.com/question/2456547

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