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Let [math]x(t)[/math] be the number of bacteria in a culture at time [math]t[/math], and let [math]x_0=x(0)[/math]. The number grows at a rate proportional to the number present, and doubles in a time interval of length [math]T[/math]. Find an expression for [math]x(t)[/math] in terms of [math]x_0[/math] and [math]T[/math], and find the average number of bacteria present over the time interval [math][0,T][/math].