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- In this video were gonna talk about actually coming up with an initial population given some information. So, after 20 minutes of growth, a population was measured and found to have 500 units. After 25 minutes of growth, its 1500. So, we want to find the initial size. To do so the main thing we need is the growth factor. So, Im gonna use the formula of the exponential Y equals A B to the T. And a slick way we can do this is we can actually act as if 20 minutes is our initial to kind of speed things along. So I can say, well, it took to go from 500 to 1500, it took five minutes. Thats enough information for me to find my base. So, Im gonna divide both sides by 500, and I get that three equals B to the fifth. Or that B equals We raise both sides to the one fifth, so three to the one fifth. Theres the base of my exponential for this model. So I know its gonna have the form Y equals A times three to the one fifth, or as I like to write it, T over five. Now, its the A that we n