Question

Solve the problem:

The number of inhabitants in millions of a certain city can be calculated using the expression
`p (x) = 2^(3) * 10(2t)/(3)` 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?

Answer 1

Given function:

• p(t) = 2³
  `10^(2t/3)`

a)

Find x when p(t) = 200:

• 2³
  `10^(2t/3)` = 200
• 
  `10^(2t/3)` = 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(
  `10^(2*4/3)` ) = 8*
  `10^(8/3)` = 3713.27 million