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1. The population of a town was 5655 in 2010. The population grows at a rate of 1.4% annually.

(a) Use the exponential growth model to write an equation that estimates the population t years after

2010.[tex]y=b(1+r)^t[/tex]

(a) Use the equation you wrote to estimate the population of the town in 2022. Show your work

Respuesta :

sqdancefan

9514 1404 393

Answer:

  (a) y = 5655(1.014^t)

  (b) y ≈ 6682

Step-by-step explanation:

(a) In the given growth mode, b is the value of the function when t=0. If we let t=0 represent year 2010, then b = 5655.

The value r is the annual growth rate when t is in years. It is given as 1.4%, so the model is ...

  y = 5655(1.014^t)

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(b) Since t is years after 2010, in 2022, t = 2022 -2010 = 12. Then the value of y is ...

  y = 5655(1.014^12) = 5655×1.18156 ≈ 6681.72

The population in 2022 is estimated to be 6682.

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