7. Bob plants a beautiful flower. Let L(t) be the length of the flower at time t (in clays). At the beginning, L(O) = 0. Bob notices that the growth rate of L(t) is E = 89\" (if. 4 ' cm/day. (a) For t 9 O, explain why L(t] is a strictly increasing function. b) Calculate the average growth rate in cm/day of the flower for the first three days (i.e. between t = O and t = 3}. c] Calculate the length in cm of the flower after the first three days (so L(SD. d) Construct a definite integral that calculates the growth of the flower over the time interval [0, b]. e} Will this flower grow infinitely if time does not stop? Explain your answer using d] and an improper integral that models the total growth of the flower