Numeracy 4. Consider the following scenario. You are given a positive numher 11]. After one minute you are told to multiply this number by R, and the new number is to he called 1'1. One minute later, you multiply P1 by H. and are to call the new numher Pg. This pattern continues forever, so that in the nth minute, we compute J"; by multiplying Pn_1 by It. 1. l[live a general expression for H; in terms of 113,3, and n, for any a E N. 2. Suppose in the above scenario that you replaced R by e', where e is Euler's number and r is a real number. After 1n minutes, you are told that P1\" = 2021. Determine the value of T which makes this true if Pa = l. 3. Suppose you are told that PD 1} and r c: ii. (a) If n. 2 1 is a natural number, is 1"\" c: I], H; = i], or P\" :a- 0. In two sentences or less, justify your answer. (b) Suppose mm are natural numbers with a \":9 m. [s 1'\" 2.2- 11.,\" P\" = P1\