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The population (in millions) of a country in 2007 and the expected continuous annual rate of change k of the population are given. † Country 2007 Population k Paraguay 6.7 0.024 (a) Find the exponential growth model P = Cekt for the population by letting t = 0 correspond to 2000. (Round numerical values to three decimal places.) P = (b) Use the model to predict the population of the country in 2013. (Round your answer to two decimal places.)

Respuesta :

sqdancefan

Answer:

  (a)  P = 5.664e^(0.024t)

  (b)  7.74 million

Step-by-step explanation:

(a) We are given the population for t=7, so we can write the equation as ...

  P = 6.7·e^(0.024(t -7))

This can be put in the desired form by factoring out 6.7e^(-0.024·7):

  P = 6.7e^(-0.024·7)e^(0.024t)

  P = 5.664e^(0.024t)

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(b) Evaluated for t=13, this is ...

  P = 5.664e^(0.024·13) ≈ 7.74 . . . million

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