# Population Growth Equation

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1. May 11, 2015

### Christo

1. The population of a certain country grows according to the formula:

N = N0e^kt

Where N is the number of people (in millions) after t years, N0 is the initial number of people (in millions) and k = 1/20 ln 5/4.

Calculate the doubling time of this population. Leave your answer in terms
of ln : Do not use a calculator.

2. I don't understand where to start off.

3. I have basically come to the conclusion that N = 2N0
That is how far I have come. I know I haven't done anything as of yet. But any help would be appreciated

2. May 11, 2015

### SteamKing

Staff Emeritus
Well, you were given a value for k. Did you plug this value into the population equation and make any obvious simplifications?

3. May 12, 2015

### symbolipoint

Use N=2 and No=1.
Take natural log of both sides of the equation.

4. May 12, 2015

### Christo

Thanks for the info, will plug in the variables and see where I end up.

5. May 13, 2015

### HallsofIvy

Staff Emeritus
To see that you get the same "doubling time" for any initial value, take $$N= 2N_0$$.