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 byguess

where is some constant. This is a differencial equation with seperable terms, thus,

Integrating,

Thus,

where

where

Notice when then is the initial amount (the starting populations) thus,

Thus, , thus,

for some .

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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,

Thus,

solve for ,

Thus,

Thus,

Thus, the formula is,