When a mutual fund company charges a fee of 0.44% on its index funds, its assets in the fund are $49 billion. When it charges a fee of 0.11%, its assets in the fund are $205 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 0.39% to 0.14%. Let R(x) denote the revenue of the company from fees when its index-fund 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. (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. A(x)=1 (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 0.39% to 0.14%. Let R(x) denote the revenue of the company from fees when its index-fund fee is x%. Compare the revenue of the company before and after lowering the fees. [Hint: Revenue is x% of the assets.] R(x) = (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) When the fees were lowered from 0.39% to 0.14%, the revenue of the company 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 maximum revenue. The fee that maximizes the revenue of the company is % (Type an integer or a decimal. Round to three decimal places as needed.) The maximum revenue of the company is $ billion. (Type an integer or a decimal. Round to three decimal places as needed.)