An elephant leaves his home at 7am. and walks along a well travelled path until he reaches a friend's home 10 hours later (where an all night elephant party ensues). The next day the elephant leaves his friend's house at 7am. and returns home in the same amount of time taking the same path. If t) represents the distance from his home on the rst day and g(t) represents the distance from his home on the second day and t represents the time in hours modulo 24 (Le. a particular t value represents the same time on any given day), prove that there is at least one time where the elephant was at the exact same spot on both days. That is, prove that there is a t": such that t\") 2 g[t"').You may assume that the elephant cannot teleport. (Hint: IVT) The Bisection Method is a rootfinding algorithm that can be conducted on a continuous function to find the root up to a given error as follows: 1. Find [or be given) an 31 and 9:2 such that Intermediate Value Theorem guarantees that f(x) = 0 on {$1,182}. :2: + :L' 2. Bisect your interval by finding the midpoint m3 = 172 3. Evaluate ora] 4. Use IVT to determine if the root is in the interval (2:1, :33) or (:33, $2}. 5. Repeat steps 2-4 until half the length of your determined interval in step 4 is less than the error you have been provided. Then, the midpoint of this determined interval is your approximated root location within the given error. Now, given the function at) : 3:3 l 5:1:2 5r: 5 and the initial interval [7, 2]: a) Show that the IVT guarantees a root on [7, 2) (so that step 1 is satisfied). b) Conduct the Bisection Method to approximate the root location (in either exact fractional or decimal form) of ea) with a maximum error of 0.4