In this problem, we will use linearization to approximate the solution of e t−1 = t 20 + 1 which occurs near t = 1.(a) (3 pts) without using a calculator, show that the equation e t−1 = t 20 + 1 must have a solution in the interval [1, 2]. you must fully justify your answer to receive full credit.(b) (3 pts) replace e t−1 by its linearization at a = 1 in the equation in part (a). solve the new equation to get an approximate solution to the original equation.