Problema Solution
A midwestern city finds its residents moving to suburbs. Its population is declining according to the function: P(t)= po e-0.04t
where t is the time measured in yrs. and po is the population at t=0. Assume that
po= 1,000,000
a) find the population at time t=1 to the nearest thousand.
b) How long to the nearest tenth of a year, will it take for the population to decline to 750,000?
c) How long to the nearest tenth of a year, will it take for the population to decline to half the initial number?
Answer provided by our tutors
P(t)= Po*e^(-0.04t)
Po= 1,000,000 is the initial number
a) find the population at time t=1 to the nearest thousand.
P(1)= 1,000,000*e^(-0.04*1)
P(1)= 1,000,000*e^(-0.04)
P(1)= 961,000 to the nearest thousand
b) How long to the nearest tenth of a year, will it take for the population to decline to 750,000?
We need to find t such that P(t) = 750,000 that is:
1,000,000*e^(-0.04t) = 750,000
e^(-0.04t) = 0.75
t = 7.2 years to the nearest tenth
c) How long to the nearest tenth of a year, will it take for the population to decline to half the initial number?
We need to find t such that:
P(t) = Po/2
P(t) = 1,000,000/2
P(t) = 500,000 that is
1,000,000*e^(-0.04t) = 500,000
e^(-0.04t) = 0.5
t = 17.3 years to the nearest tenth