The population P, in hundreds, of a small mining town in the California Gold Rush, is given by the function P =f(t), where t is in years since 1850. Use the graph of f(t) to answer the following. a) When did the population of the town reach zero? b) Find two different time intervals for which the average rate of change of P with respect tot 0 2 4 6 8 1 12 was zero. a) The year the population of the town reached zero is b) Using the points indicated on the graph of f(t), the interval with the shorter time span where the average rate of change was zero is from the year Using the points indicated on the graph of f(t), the interval with the longer time span where the average rate of change was zero is from the year to the year , a span of years. to the year , a span of years. Find an equation for the tangent line to the graph of the given function at (5,33). f(x) = x2 + 8 E) Find an equation for the tangent line to the graph of f(x) = x2 + 8 at (5,33). FD The daily demand, q, for cupcakes is a function of the price p, where q = f(p) = 170 - 40p. a. Find and interpret f(2). b. Find and interpret f"(2). lnterpret f(2) = 90 in economic terms. When cupcakes sell for $|:| each, there will be |:| sold that day. @ lnterpret f'(2 )= -40' In economic terms. Lowering the price from $|:| to $|:| would cause a(n) |:| in sales of D cupcakes