precalculus
posted by steve alexander .
the population of a country is 65 millions if it grows exponentially in a rate of 1.5% annual
1.calculate the estimate population in 12 years
2.when the population increases 4 times
could somebody please explain me this kind of problems where you need to use the log and please tell me the answers

1. .015*65*12+65=76.7 million
2. 4*65=260 million 
1. Multiply 65 million by (1.015)^12
(1.015^12 = 1.1956)
2. Multiply 65 million by 4.
You don't need to use log for the second one.
You can to 1. with a log table or with a hand calculator (as I did).
If you use logs:
Log (answer) = log (65 million) + 12 log 1.015
Then take the antilog
You will learn more if you do the calculations yourself than if I gave you the numerical answers. 
Let
P = population in millions
t = time in years
Population growth is continuous. For continuous compounding use the formula:
P = 65*e^(.015t)
For the population in 12 years we have:
P = 65*e^(.015*12) = 65*e^(.18)
P = 77.8 million