When a mutual fund company charges a fee of 0.42% on its index funds, its assets in the fund are $34 billion. When it charges a fee of 0.16%, its assets in the fund are $202 billion. (a) Let x denote the fee that the company charges as a percentage of the index fund and letA(x) denote its assets in the fund. Express Atx) as a linear function of x. (b) One company lowers its fees on various index funds from an average of 0.32% lo 0.09%. Let R(x) denote the revenue of the company from fees when its indexfund fee is x%. Compare the revenue of the company before and after lowering the fees. [Hint: Revenue is x% of the assets] (c) Find the fee that maximizes the revenue of the company and determine the maximum revenue. / ..... N (a) Let x denote the fee that the company charges as a percentage of the index fund and letA(x) denote its assets in the fund. Express A(x} as a linearfunction of x. A(x) = (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) (b) One company lowers its fees on various index funds from an average of 0.32% to 0 00%. Let R(x) denote the revenue of the company from fees when its indexfund fee is x%. Compare the revenue of the company before and after lowering the fees. [Hint: Revenue is x% of the assets] Rm 2 (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) When the fees were lowered from 0.32% to 0.09%, the revenue of the company (Type an integer or a decimal. Round to three decimal places as needed.) Y by$ (c) Find the fee that maximizes the revenue of the company and determine the maximum revenue. The fee that maximizes the revenue of the company is % ("ype an integer or a decimal. Round to three decimal places as needed.) The maximum revenue of the company is 55 billion. ("ype an integer or a decimal. Round to three decimal places as needed.) billion