Hello, camjenson!

A colony of people grows at a rate directly proportional to the size of the population.

The colony triples every two hours.

1. (a) Write differential equation that describes the colony's growth.

. . (b) Find the general solution.

(b) We have: .

Integrate: .

Hence: .

When , the initial population.

So we have: .

Therefore, the equation is: .

2. What's the value of the constant of proportionality?

The population triples every two hours.

When

We have: .

. . . . . . . .

3. At t = 9 hours, the population is 800 million, what is the initial population?

The equation is: .

And we have: .

When

. .

. .