The populations P in thousands of a city from 2000 to 2003 c

The populations P (in thousands) of a city from 2000 to 2003 can be modeled by P = 2480e^- 0.0022 t, where t represents the year, with t = 0 corresponding to 2000. (a) According to the model, was the population increasing or decreasing from 2000 to 2003? increasing decreasing (b) What were the populations of the city in 2000 and 2002? (Round your results to three decimal places each.) 2000 P = 2400 thousand people 2002 P = 2469.112 thousand people (c) According to the model, when will the population be approximately 2.4 million? (Enter the calender year.)

Solution

P=2480 e^-0.0022t

Since the e have negative exponent , so its decreasing .

b. In 2000, t=0

P=2480 e⁰=2480

In 2002, t=2

P=2480e^-.0022*2=2469.112