The birth rate in a certain city is described by the following function
.
The city's death rate is given by
.
Here,
t is measured in years, and
t = 0 corresponds to the start of the year 1990. The birth and death rates are measured in thousands of births or deaths per year. At the start of 1990, the population of the city is 450 thousand.
A) Calculate the total number of births between the start of 1990 and the end of 1999.
B) Calculate the total number of deaths over the same period.
C) What is the population of the city at the start of year 2000?
D) Considering just the period from the start of 1990 to the start of 2000, over what interval is the population increasing?
E) Over what interval is the population decreasing?
F) Calculate the area between the curves
y =
b (
t ) and
y =
d (
t ) for
t between 0 and 10. Area :_________
For this problem I tried to use the formula
P(t) = Yo e^kt
Yo =450 at t=0
P(t) = 450 e^k(0)
I set the birth and death rates equal
=
When t = 4, they are equal at 5.16
For part F I found the anti derivatives
At the start of 2000 (t =10) the birth rate is 1.8 and death rate is 6.
At 2008 (t =8) the birth rate is 3.24 and death rate is 5.64.