9. If a variable x is exponentially distributed with the following probability density function, what is the expected value of x?( 5%) 
(A) e²
(B) 2 
(C) 0.5
(D) None of the above

1. (5%) Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by . Find the tax rate t that maximizes revenue for the government. (A)3.6% (B) 6.4% (C) 9.2% (D) None of the above

2. (5%) The capital value of an asset (such as an oil well) that produces a continuous streamn of income is the sum of the present values of all future earnings from the asset. Therefore, the capital value of an asset that produces income of r(t) dollars at time t (discounted at a continuous interest rate t) is where T is the expected life (in years) of the asset. For an oil well that produces income of r(t) = 10000t2 for the following 10 years and the interest rate i = 5%, what is the capital value of this oil well? (A) 2,302,028 dollars (B) 99,346,934 dollars (C) 26,563,254 dollars (D) None of the above

3. (5%) What is the solution form of A(t) if A'(t) = A2(t)- 1,and A(0) = 0. (A) A(t) = a + bect (B) A(t) = (a + bect)-1 (C) A(t) = (at bect)-1 + d (D) None of the above

4. (5%) Solve the function A(t) in Question (3). What is the value of A(1)? (A) 1.2976 (B) -0.2976 (C) -0.7616 (D) None of the above

5. (5%) A company's production is given by the Cobb-Douglas function P=60L2/3K1/3, where L and K are the number of units of labor and capital. Each unit of labor costs $25 and each unit of capital costs $100. The company wants to produce exactly 1920 units. Find L* and K* that meet the production requirements at the lowest cost. What is the value of L* + K*? (A) 64 (B) 72 (C)80 (D) None of the above

6. What is the value of?(5%) (A) 2 (B) 1 (C)0 (D) None of the above

7. What is the value of (5%) (A)∞ (B) -In1 (C) -In2 (D) -∞

8. What is the value of dxdy? (5%) (A) e2-3 (B) (C) e2+2 (D) None of the above

10.(5%) Find the maximum value of f(x,y)=cosx+cosy subject to the constraint condition (A) (B) (C) (D) None of the above 

10. 以下四個圖與所對應的方程式, 何者為錯。 (A) (B) (C)(D)

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