the population P, in thousands, of a small city is given by, P(t)=500t/2t^+9 , where t is the time in years. find the population after 10 months

Answer 1

Solution:

P(t) = (500 t) / (2t²+9) since t is in years and you are given that t = 10 month, then

t = 10 month ( years/ 12 month) = 0.83 years or 5/6 years

Since the function P(t) is in terms of time in years then substitute 0.83 years for t in the equation

P(0.83) = [ (500)(0.83) / 2(0.83)² +9 ] = 415 / 10.378 = 39.98 (1000 ) = 39,980 or approximately 40,000