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Sally makes deposits into a retirement account every year from the age of 30 until she retires at age 65 . a) If Sally deposits 1200 per year and the account earns interest at a rate of \(8 \%\) per year, compounded annually, how much does she have in the account when she retires? (Hint: Use the annuity formula for Exercises 35 and 36 . ) b) How much of that total amount is from Sally's deposits? How much is interest?

Use the vertical-line test to determine whether each graph is that of a function. (The vertical dashed lines are not part of the graph.)

Consider the function \(\int\) given by $$ f(x)=\left\\{\begin{array}{ll} -2 x+1, & \text { for } x<0 \\ 17, & \text { for } x=0 \\ x^{2}-3, & \text { for } 0

Suppose that \(\$ 5000\) is invested at \(8 \%\) interest, compounded semi annully, for \(t\) years. a) The amount \(A\) in the account is a function of time. Find an equation for this function. b) Determine the domain of the function in part (a).

Rewrite each of the following as an equivalent expression with rational exponents. $$\frac{1}{\sqrt{x^{2}+7}}$$

Suppose that \(\$ 3000\) is borrowed as a college loan, at \(5 \%\) interest, compounded daily, for \(t\) years. a) The amount \(A\) that is owed is a function of time. Find an equation for this function. b) Determine the domain of the function in part (a).

The amount of money, \(A(t),\) in a savings account that pays \(6 \%\) interest, compounded quarterly for \(t\) years, with an initial investment of \(P\) dollars, is given by $$A(t)=P\left(1+\frac{0.06}{4}\right)^{4 t}$$ If \(\$ 500\) is invested at \(6 \%\), compounded quarterly, how much will the investment be worth after 2 yr?

Boxowitz, Inc., a computer firm, is planning to sell a new graphing calculator. For the first year, the fixed costs for setting up the new production line are 100,000 dollars. The variable costs for producing each calculator are estimated at 20 dollars. The sales department projects that 150,000 calculators can be sold during the first year at a price of 45 dollars each. a) Find and graph \(C(x),\) the total cost of producing \(x\) calculators. b) Using the same axes as in part (a), find and graph \(R(x),\) the total revenue from the sale of \(x\) calculators. c) Using the same axes as in part (a), find and graph \(P(x),\) the total profit from the production and sale of \(x\) calculators. d) What profit or loss will the firm realize if the expected sale of 150,000 calculators occurs? e) How many calculators must the firm sell in order to break even?

Red Tide is planning a new line of skis. For the first year, the fixed costs for setting up production are 45,000 dollars. The variable costs for producing each pair of skis are estimated at 80 dollars, and the selling price will be 255 dollars per pair. It is projected that 3000 pairs will sell the first year. a) Find and graph \(C(x),\) the total cost of producing \(x\) pairs of skis. b) Find and graph \(R(x),\) the total revenue from the sale of \(x\) pairs of skis. Use the same axes as in part (a). c) Using the same axes as in part (a), find and graph \(P(x),\) the total profit from the production and sale of \(x\) pairs of skis. d) What profit or loss will the company realize if the expected sale of 3000 pairs occurs? e) How many pairs must the company sell in order to break even?

In computing the dosage for chemotherapy, a patient's body surface area is needed. A good approximation of a person's surface area \(s\), in square meters \(\left(m^{2}\right),\) is given by the formula $$s=\sqrt{\frac{h w}{3600}}$$ where \(w\) is the patient's weight in kilograms (kg) and h is the patient's height in centimeters (cm). (Source: U.S. Oncology.) Use the preceding information . Round your answers to the nearest thousandth. Assume that a patient's height is 170 cm . Find the patient's approximate surface area assuming that: a) The patient's weight is 70 kg. b) The patient's weight is 100 kg. c) The patient's weight is 50 kg.