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Solve the problem:

The number of inhabitants in millions of a certain city can be calculated using the expression [tex]p (x) = 2^{3} * 10\frac{2t}{3}[/tex] If t represents time in years:

a) How long approximately must elapse for the population of the city to be 200 million inhabitants?

b) How many inhabitants will be in the city after 4 years?

Respuesta :

mhanifa

Answer:

Given function:

  • p(t) = 2³[tex]10^{2t/3}[/tex]

a)

Find x when p(t) = 200:

  • 2³[tex]10^{2t/3}[/tex] = 200
  • [tex]10^{2t/3}[/tex] = 252
  • 2t/3 = log 25
  • t = 3 log 5
  • t = 2.0969 years ≈ 2 years and 1 month

b)

Find p(t) when t = 4:

  • p(4) = 2³([tex]10^{2*4/3}[/tex] ) = 8*[tex]10^{8/3}[/tex] = 3713.27 million

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