CPM Homework Help : CALC3RD Problem 7-103

Population growth is proportional to the current population. For example, if a town has $100$ people, its change in population for a year will be based on those $100$ people. Therefore, its change will be much smaller than that of a large city like San Francisco, with population $800,000$ . Why? Write down your reasoning

Step 1:

$\text{Let }P(t) =\text{ current population and }\frac{dP}{dt}=\text{ population growth}.$

Step 2:

If population growth is proportional to current population, set up a proportional equation to model this statement.
Remember the constant of proportionality.

Hint:

$\text{This function, }P,\text{ is equal to its derivative, }\frac{dP}{dt}\text{ times a constant.}$

What 'type' of function must it be?
Is it: linear, quadratic, trigonometric, exponential, or something else?