Question

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

Answer 1

1. .015*65*12+65=76.7 million
2. 4*65=260 million

Answer 2

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.

Answer 3

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