Respuesta :
Answer:
Population of the city after 7 years from now, P(7) = 6370
Given:
Initial Population, [tex]P_{i} = 31000[/tex]
rate, r(t) = 1200 /yr
S(t) = [/tex]\frac{1}{1 + t}[/tex]
Step-by-step explanation:
Let the initial population be  [tex]P_{i} = 31000[/tex]
The population after T years is given by the equation:
[tex]P(T) = P_{i}S(T) + \int_{0}^{T}S(T - t)r(t) dt[/tex] Â Â Â Â Â (1)
Thus, the population after 7 years from now is given by using eqn (1):
[tex]P(7) = \frac{3100}{1 + 7} + 1200\int_{0}^{7}\frac{1}{8 - t} dt[/tex]
[tex]P(7) = 3875 - 1200ln(8 - t)|_{0}^{7}[/tex]
[tex]P(7) = 3875 - 1200ln(8 - t)|_{0}^{7}[/tex]
[tex]P(7) = 3875 - 1200(ln(1) - ln(8))[/tex]
[tex]P(7) = 3875 + 2495 = 6370[/tex]
