In 1980, the population of the country Alford was 50,000 people and since was in
ID: 2912688 • Letter: I
Question
In 1980, the population of the country Alford was 50,000 people and since was increasing continuously by 5.5% per year for the next 30 years. On the other hand, the population of the country Olag was 60,000 and increasing by 3,000 people per year over the same time period.
A. For each country, write a formula expressing the population as a function of time t, where t is the number of years since 1980.
B. Approximately, what was the population of each country in 2008?
C. In how many years will the population of Alford reach approximately 75,000? (Use logs to solve)
D. In what year will the population of Alford surpass the population of Olag? (Solve graphically)
Explanation / Answer
a) formula for Alford
P = 50000 e^.055t
formula for Olag
P = 3000 t + 60000
b) population of Alford in 2008
P = 50000 e^.055(28)
P = 233229.5
population of Olag in 2008
P = 3000 (28) + 60000
P = 144000
c) 50000 e^.055t = 75000
t = 7.37
so,in 7.37 years population of alford will be 75000
3000 t + 60000 = 75000
t = 5
in 5 years population of Olag will be 75000
d) 50000 e^.055t > 3000 t + 60000
t > 3.12
so, after 3.12 years Alford will surpass Olag