11.1 years
The phrase "increase at a rate proportional to the number of people present" is a rather wordy way is saying "the population grows at a geometric rate". Or "the growth rate is exponential" and that last statement is the critical one. Let's take the log of 2 and divide by 7
log(2)/7 = 0.30103 / 7 = 0.043004
Now if you calculate 10^0.043004, you'll get 1.10409 which is how much the population is increasing each year. But you don't need that number. Instead, take the log of 3 and divide by the 0.043004 figure you got earlier.
log(3)/0.043004 = 0.477121255/0.043004 = 11.09474
So it will take 11.1 years for the population to triple. Let's check that by raising 1.10409 to the 7th and 11.1 powers.
1.10409^7 = 2.0000
The above confirms that the rate of 1.10409 properly doubles the population in 7 years.
1.10409^11.1 = 3.00
And that same growth rate will triple the population in 11.1 years.
