2. (a) (i) Use the linear approximation formula y m f '[m] be: 01' fl=r+=l \"r: fli\") +f'lml-T with a suitable choice of r} to show that s"!2 m 1 + 92 for small values of H. 134 {ii} Use the result obtained in part (a) above to approximate f 3'92 d3. 0 1;"! (iii) Approximate f e92 (in? using Simpson's rule with n = 8 strips. 0 How does the approximate answer in (iii) compare with the approximate answer in (ii)? {b} If A0 dollars are initially invested in a bank account which pays yearly interest at the rate of 9:%, then after an years the account will contain 11., = Ag{1 +9: f 100)" dollars. The amount of money in the account will double {i.e. A\" = 2 A43} when log 2 =log(1 + mleU')' (i) Use the linear approximation formula given above (in part (a)(i)] with a suitable choice of x) to show that log(1 + 3/100) "m" %. {ii} Hence, show that the number of years n for the sum of money to double is given approximately by N 100mg? 70 any~ r .9: A {This is known as the \"Rule of 70\".)