thanks!

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- Nov 11th 2012, 09:06 PMcamjensonGrowth problem? Any help would be greatly appreciated!
thanks!

- Nov 11th 2012, 10:01 PMSorobanRe: Growth problem? Any help would be greatly appreciated!
Hello, camjenson!

Quote:

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: .

Quote:

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

The population triples every two hours.

When

We have: .

. . . . . . . .

Quote:

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

The equation is: .

And we have: .

When

. .

. .