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- Prove that bx=exln(b) for positive b1 .Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [2, 4]