This is a classical differencial equation. It is a mathematical model based on growth-which is exponential. Let be a function which show the population at any given time. By the rule of growth:Originally Posted by guess
where is some constant. This is a differencial equation with seperable terms, thus,
Notice when then is the initial amount (the starting populations) thus,
Thus, , thus,
for some .
Solve the problem, 4th day was 350 and 5th was 500.
Substitute that infromation into the exponential equation,
Divide the second equation by the first to get,
solve for ,
Thus, the formula is,