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in this video were going to talk about exponential growth and decay problems as it relates to population growth so to speak now the first equation you need to be familiar with is this equation dp divided by dt is equal to k times p so this equation tells us that the population grows at a rate that is proportional to the size of the population the population growth rate is dpdt thats how fast the population is grown at a given time k is the relative growth rate and p is the size of the population at some time t now to understand this conceptually lets say if we have a sample of a thousand bacteria and lets say that in this sample the bacteria grows 50 cells per hour whats going to happen if we double the population lets say if we have a sample of 2 000 bacteria counts well since we have twice the amount of bacteria we should expect it to grow at twice the rate that is at 100 cells per hour so thus we could see that the rate at which the population grows is proportional to the pop
