Consider the production of gold during the California gold rush (1848–1888). The production of gold can be modeled by $G(t)=\frac{(25 t)}{\left(t^{2}+16\right)},$ where t is the number of years since the rush began $(0 \leq t \leq 40)$ and G is ounces of gold produced (in millions). Find when the minimum (local and global) gold production occurred. What was the amount of gold produced during this minimum?

Describe a gratuity and explain why this custom is practiced at restaurants.

Sketch the graph of a function that has two local maxima, one local minimum, and no absolute minimum.

Sketch the graph of a function that has three local minima, two local maxima, and seven critical numbers.

(a) If b is a positive constant and x > 0, find all critical points of f(x) = x - b ln x. (b) Use the second-derivative test to determine whether the function has a local maximum or local minimum at each critical point.

Is the environmental impact of big cities all positive, all negative, or neither? Explain.

Write the fraction or mixed number as a percent. $8 \frac{9}{25}$

A figure has vertices F(-1,1), G(1,1), H(2,-1), and I(-1,-1). Graph the figure and the image of the figure after a dilation with a scale factor of 3.

How are the sun, Earth, and the moon aligned when spring tides occur? (Hint: Recall during which phases of'fhe moon spring tides occur.) A. The sun, Earth, and the moon form a straight Line. B. The sun, Earth, and the moon form a 45-degree angle. C. The sun, Earth, and the moon form a 90-degree angle. D. The sun, Earth, and the moon form a 135-degree angle.

How would you rate the overall healthfulness of this food selection? What might this suggest about food and emotions?

Explain how consuming an acid-neutralizing antacid might affect protein digestion. Apply the concept of activation energy to support your explanation.

Determine whether the equation defines y as a function of x. $x=y^{2}$

You are evaluating two companies as possible investments. The two companies, which are similar in size, are commuter airlines that fly passengers up and down the West Coast. All other available information has been analyzed, and your investment decision depends on the statements of cash flows. Blue Yonder Airlines Statements of Cash Flows Years Ended November 30, 2013 and 2012

$$\begin{matrix} \quad & 2013 & \quad & 2012 & \quad\\ \text{Operating activities: } & \quad & \quad & \quad & \quad\\ \text{Net income (net loss) } & \quad & \text{\$(63,000)} & \quad & \text{\$160,000}\\ \text{Adjustments for non-cash items:} & \quad & \quad & \quad & \quad\\ \text{Total } & \quad & \text{79,000 } & \quad & \text{(13,000) }\\ \text{Net cash provided by operating activities} & \quad & \text{16,000} & \quad & \text{147,000}\\ \quad & \quad & \quad & \quad & \quad\\ \text{Investing activities:} & \quad & \quad & \quad & \quad\\ \text{Purchase of property, plant, and equipment} & \text{\$ (67,000)} & \quad & \text{\$(140,000) } & \quad\\ \text{Sale of long-term investments } & \text{58,000} & \quad & \text{9,000} & \quad\\ \text{Net cash provided by (used for) investing activities } & \quad & \text{(9,000)} & \quad & \text{(131,000)}\\ \quad & \quad & \quad & \quad & \quad\\ \text{Financing activities: } & \quad & \quad & \quad & \quad\\ \text{Issuance of short-term notes payable } & \text{\$ 198,000 } & \quad & \text{\$ 218,000 } & \quad\\ \text{Payment of short-term notes payable } & \text{(246,000) } & \quad & \text{(183,000) } & \quad\\ \text{Payment of cash dividends } & \text{(51,000)} & \quad & \text{(92,000)} & \quad\\ \text{Net cash provided (used) by financing activities } & \quad & \text{(99,000) } & \quad & \text{(57,000) }\\ \text{Increase (decrease) in cash} & \quad & \text{\$(92,000) } & \quad & \text{\$ (41,000) }\\ \text{Cash balance at beginning of year } & \quad & \text{106,000 } & \quad & \text{147,000}\\ \text{Cash balance at end of year} & \quad & \text{\$ 14,000} & \quad & \text{\$106,000}\\ \end{matrix}$$

Horizon, Inc. Statements of Cash Flows Years Ended September 30, 2013 and 2012

$$\begin{matrix} \quad & \text{2013} & \quad & \text{2012} & \quad\\ \text{Operating activities: } & \quad & \quad & \quad & \quad\\ \text{Net income (net loss) } & \quad & \text{\$ 264,000} & \quad & \text{\$ 193,000}\\ \text{Adjustments for non-cash items:} & \quad & \quad & \quad & \quad\\ \text{Total } & \quad & \text{67,000 } & \quad & \text{79,000 }\\ \text{Net cash provided by operating activities} & \quad & \text{331,000} & \quad & \text{272,000}\\ \quad & \quad & \quad & \quad & \quad\\ \text{Investing activities:} & \quad & \quad & \quad & \quad\\ \text{Purchase of property, plant, and equipment} & \text{\$(395,000)} & \quad & \text{\$(610,000) } & \quad\\ \text{Sale of property, plant, and equipment} & \text{69,000} & \quad & \text{119,000} & \quad\\ \text{Net cash used for investing activities} & \quad & \text{(326,000)} & \quad & \text{(491,000)}\\ \quad & \quad & \quad & \quad & \quad\\ \text{Financing activities: } & \quad & \quad & \quad & \quad\\ \text{Issuance of long-term notes payable } & \text{\$ 198,000 } & \quad & \text{\$ 131,000 } & \quad\\ \text{Payment of short-term notes payable } & \text{(95,000)} & \quad & \text{(26,000)} & \quad\\ \text{Net cash provided by financing activities } & \quad & \text{103,000 } & \quad & \text{105,000 }\\ \text{Increase (decrease) in cash} & \quad & \text{\$ 108,000 } & \quad & \text{\$ (114,000) }\\ \text{Cash balance at beginning of year } & \quad & \text{176,000 } & \quad & \text{290,000 }\\ \text{Cash balance at end of year} & \quad & \text{\$ 284,000} & \quad & \text{\$ 176,000}\\ \end{matrix}$$

Discuss the relative strengths and weaknesses of Blue Yonder Airlines and Horizon, Inc. Conclude your discussion by recommending one of the companies’ stocks as an investment.

Sketch the graph of a function on [0, 4] having (a) Two local maxima and one local minimum. (b) An absolute minimum that occurs at an endpoint, and an absolute maximum that occurs at a critical point.