A scientist studying insect starts with a population of 10. The population triples every hour. How many insects with be there in 20 minutes.

The question is asking you to understand that a population which is raised by a common ratio over a certain time period follows an exponential pattern. See:

After 1 hour, the population is 3*10

After 2 hours, the population is 3*3*10

After 3 hours, the population is 3*3*3*10

...

This can be generalised as a function of t, the time in hours:

f (t) = (3^t) * 10

Since the function determines the population at a given time, it is more prudent to replace f (t) with P, the population after time t:

P = (3^t) * 10

Since 20 minutes is equal to (1/3) hours, t can be substituted for (1/3) in order to calculate the population size after 20 minutes:

P = (3^ (1/3)) * 10 = 14.4224957031 ≈ 14

Therefore the population after 20 minutes is 14.