If y (t) grows continuously at a constant rate g and we know an initial\ condition y (0), then the value of y (t) at time t is given by y (t) = y (0) egt,\ where e represents the exponential function. Taking logs of both sides we obtain\ log (y (t)) = log (y (0)) + gt,\ which says that log(y (t)) is a linear function of time, with the slope of the\ line equal to the growth rate, g.\ (a) Starting from the expressions above, show that the growth rate of\ y (t) is indeed g.\ (b) On two separate graphs, plot the values of y (t) and log(y (t)) for the following values of the growth rate: g = 0.02, g = 0.05, and g = 0.1, given an initial value y (0) = 1.