The populations P in thousands of Pittsburgh Pennsylvania fr

The populations P (in thousands) of Pittsburgh, Pennsylvania from 1990 to 2004 can be modeled by the following where t is the year, with t = 0 corresponding to 1990. P = 372.55e^–0.01052t

(c) According to the model, when will the population be approximately 280,000?

(b) What were the populations of Pittsburgh in 1990, 2000, and 2004? (Round your results to 3 decimal places each.)

Solution

(a) 280,000 = 372550 e^(-0.01052 t)
0.751577 = e^(-0.01052 t)
-0.285582 = -0.01052 t
t = 27.15 years

(b) P (1990) = 372,550
P (2000) = 372,550 e^(-0.1052) = 335348.8
P (2004) = 372,550 e^(-0.1052 x 1.4) = 321530.13