thanks!
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
. .
. .