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QMB 3003 - Final Exam
The demand curve is Q = 116 - 11P. At a price of $5 find the elasticity of demand. - Answer- A line passes through the points (10, 21) and (29,52). What is the slope of the line? - Answer-1. Which of the following best describes the second derivative? - Answer-The second derivative helps determine the rate of change of the first derivative. Consider the demand function for good Z as given by QDz = f(Pz, Y, Px) = 305 - 2Pz - 0.005Y + 3Px. Find the following partial derivative: fY(Pz, Y, Px) = - Answer- When interest is compounded more than once per year then the effective interest rate is lower than the annual interest rate. - Answer-False A firm finds its sales increased from 2.25 million units to 2.87 million units last year. What was the percentage change in sales? - Answer-27.
Suppose f(x) has a relative minimum at x = 100. At a value of 95 we can expect f'(x) to have a negative value. - Answer-True At the break-even quantity, which of the following is true? - Answer-Revenue=Cost Which of the following cannot have a negative value? - Answer-Total Cost What is the first derivative of f(x) = x/2? - Answer-1/ Find the partial derivative of f(x,y) with respect to x and evaluate at x = 7 and y = 4. Find fx(x,y) if f(x,y) = 4x2 + 5x2y + 12xy2. - Answer- Elasticity of demand is calculated as percentage change in quantity demanded divided by percentage change in price. - Answer-True The profit (in thousands of dollars) from expenditure of x thousand dollars on advertising is given by P(x) = 2,000 + 64x - 4x^2. The firm is presently spending $7,000 on advertising. Which of the following is true? - Answer-The slope of the profit function is positive The partial derivative of z = f(x,y) with respect to x is the rate of change of z with respect to x if y is held constant. - Answer-True Find the derivative of y = ln(4x + 7). - Answer-4/(4x + 7) Find the amount that should be invested now to accumulate $43,342 at an annual interest rate of 7.13% compounded annually for 14 years. - Answer-16,525.
Sales at company X increased by 3.2% last year. We can conclude revenue earned from sales must also have increased. - Answer-False A person deposits $2,000 for 6 years in an account that pays 8.4% per year compounded quarterly. - Answer-What is the interest rate per period? Correct answer: 2.1% How many compounding periods are there? Correct answer: 24 How much is in the account at the end of the 6 years? $ Correct answer: 3293. The first derivative test can be used to determine whether a critical number represents a relative maximum or a relative minimum for a function. - Answer-True Consider the function f(x) = 2x^3 - 3x^2 - 72x + 15. On what interval is this function decreasing? - Answer-(-3, 4) Consider the function f(x) = 95 + 10/x for all positive values of x. - Answer- Consider the function y = f(x, z) = 100 - 2x + 3z. Which is true? - Answer-This function is decreasing in x and increasing in z Consider the function y = f(x, z) = 500 - 3z + 2x. Which is true? - Answer-
Find the annual interest rate: You deposit $3,976 and it increases in value to $4,689.37 over a period of 11 years compounded semiannually. - Answer-1. A firm's sales are 2.28 million in 2021 and 2.69 million in 2022. What was the percentage change in sales? - Answer- If y = 5e^0.4x find the derivative and evaluate at x = 3. - Answer-6. If y = e-2x find the derivative. - Answer--2e2x^-2e If y = 10ln(6x2) find the derivative and evaluate at x = 10. - Answer- Find the derivative of y = ln(4x + 7) and evaluate at x = 2.9. - Answer-0. Consider a function f(x). If f'(x) > 0 then the function f(x) is increasing. - Answer-True Consider the function y = 100 + 4x. Which is true? - Answer- If f'(c) = 0 then c is called a critical number. - Answer-True If y = ln(8x) find the derivative. - Answer-1/x Suppose f(x) attains its maximum value at x = 120. For values of x < 120 we can expect f'(x) to have a positive value. - Answer-True
Find the rate of change of A with respect to r. Do not convert r to a decimal. Round to two decimal places. - Answer- Find the compound amount: $4,482 deposited at a 6% annual rate compounded quarterly for5 years. Round to two decimal places. - Answer- A research group finds the percent of full attention that a viewer devotes to a commercial is a function of time (in seconds) since the commercial began. Assume the commercial is 30 seconds. Viewer's attention = f(t) = -0.15t^2 + 6t + 20. The commercial's main message should be presented at - Answer- A company has a cost function C(q) = 100 + 10q and a demand function p = D(q) = 50 - 2q. To maximize profit the company should charge a price of $ - Answer- The firm finds its revenue earned from advertising is TR = 14x - 2x2, where x represents hours of advertising per week. The cost of advertising is TC = 2x + 10. To maximize the profit earned from advertising hours the firm should choose to advertise - Answer-
The profit (in thousands of dollars) from the expenditure of x thousand dollars on advertising is given by P(x) = 1,000 + 35x - 8.0x^2. The firm should choose to spend $___ thousand on advertising. - Answer-2. The revenue generated by the sale of x picnic tables is R(x) = 24x - (x2/488). Find the marginal revenue when x = 990. - Answer-19. Find the derivative of y = 15x3 + 17x2 and evaluate the derivative at x = 2. - Answer- A firm finds that when it produces 90 units of output per week, its revenue is maximized. In this case its marginal revenue will be equal to zero. Correct answer: - Answer-True If f(x) = 20 then f'(x) = 20. - Answer-False The marginal revenue function MR(q) identifies the instantaneous change in revenue R(q) for a given value of sales (q) - Answer-True The profit (in thousands of dollars) from expenditure of x thousand dollars on advertising is given by P(x) = 1,000 + 32x - 2x^2. If the firm is presently spending $6,000 on advertising (x = 6) should they increase their spending? - Answer-Yes The revenue generated by the sale of x picnic tables is R(x) = 20x - (x2/500).
The larger of the two values is Correct Answer: 2 . Suppose the demand function is given by P = 10 - 2Q. Which of the following defines the revenue function R(Q)? - Answer-R(Q) = 10Q - 2Q At the revenue maximizing quantity, the slope of the revenue function is equal to zero. - Answer-True Which of the following can have a negative value? - Answer-Marginal Revenue The derivative of a quadratic function is also a quadratic function. - Answer-False What is the derivative of f(x) = 1/x2? - Answer--2/x^ The slope of the tangent line to f(x) at x = a is equal to f'(a). - Answer-True What is the derivative of f(x) = 8x^2? - Answer-16x Suppose the profit function is quadratic. At the current level of production we find the slope of the profit function is positive. In this case we should reduce our level of production in order to earn a higher profit.
- Answer-False The derivative of f(x) represents the instantaneous rate of change of y = f(x) with respect to x. - Answer- True
Find the derivative of y = 6x3 + 15x2 and evaluate the derivative at x = 3. - Answer-The value of the derivative is 252
