When a mutual fund company charges a fee of0.45% on its index funds, its assets in the fund are $32 billion. When it charges a fee of 0.12%, its assets in the fund are $236 billion. (a) Let x denote the fee that the company charges as a percentage of the index fund and let A(x) denote its assets in the fund. Express A(x) as a linear function of x. (b) One company lowers its fees on various index funds from an average of 0.27% to 0.07%. 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 ofthe index fund and let A(x) denote its assets in the fund. Express A(x) as a linearfunction of x. A(x)= 513.333x +202.133 (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 ofh.2T% to 0.0?%. Let R(x) denote the revenue of the company from fees when its indexefund fee is x%. Compare the revenue of the company before and after lowen'ng the fees. [Hinti Revenue is x% of the assets] R(x) = a 5.1333):2 +2.82133x (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) When the fees were lowered from 0.27% to 0 07%. the revenue of the company V by $ billion. (Type an integer or a decimal. Round to three decimal places as needed.) (c) Find the fee that maximizes the revenue of the company and determine the m - The fee that maximizes the revenue of the company is \"xi: decreased (Type an integer or a decimal. Round to three decimal places as needed.) increased The maximum revenue of the company is 3% billion. (Type an integer or a decimal. Round to three decimal places as needed.)