Solve

Joe Norstrom lost $\$ 400$ on each of seven consecutive days in the stock market. Represent his total loss as a product of signed numbers and find his total loss.

The weekly marginal revenue from the sale of x pairs of tennis shoes is given by $R^{\prime}(x)=40-0.02 x+\frac{200}{x+1} \quad R(0)=0$ where R(x) is revenue in dollars. Find the revenue function. Find the revenue from the sale of 1,000 pairs of shoes.

In 2010, the United States alone accounted for 20.2% of the world’s total energy consumption, using 103.3 quadrillion British thermal units (Btu). What was the world’s energy consumption in 2010? Round to the nearest quadrillion.

In 2012, U.S. consumption of renewable energy was 8.45 quadrillion Btu (or $8.45 \times 10^{15} \mathrm{Btu}$ ). since the 1960 s, consumption has been growing at a rate (in quadrillion Btu per year) given by $f^{\prime}(t)=0.004 t+0.062$ where t is years after 1960. Find f(t) and estimate U.S. consumption of renewable energy in 2024.

Find the indefinite integral. (Check by differentiation.)

$$\displaystyle{\int}\frac{1-y^{2}}{3y}\ dy$$

In 1970 the United States produced 63.5 quadrillion BTU (British Thermal Units) of energy and consumed 67.86 quadrillion BTU. From 1970 through 2001, the total U.S. energy production increased by about 0.2813 quadrillion BTU per year, and the total U.S. energy consumption increased by about 0.912 quadrillion BTU per year. a. Write two equations that model the total U.S. energy production and consumption (in quadrillion BTU) as functions of the number of years since 1970. b. How much more energy was consumed than produced in the U.S. in 1970 and in 2001? What was the change in the amount of energy consumed from 1970 to 2001?

Calculate. $\int{x(1+x)^{1/3}}dx$

Solve

A football team lost four yards on each of three consecutive plays. Represent the total loss as a product of signed numbers and find the total loss.

Perform the indicated operations. $\frac{-3-2(-9)}{-15-3(-4)}$

Quarterly revenue ($millions) for Twitter for the first quarter of 2012 through the first quarter of 2014 are shown below (adexchange.com, April, 2015):$

$$\begin{array}{cc} \text { Quarter } & \text{ Revenue (\$ millions) } \\ 1 & 54 \\ 2 & 68 \\ 3 & 82 \\ 4 & 112 \\ 5 & 114 \\ 6 & 139 \\ 7 & 169 \\ 8 & 243 \\ 9 & 250 \end{array}$$

$

a. Create a time series plot. What kind of pattern can be found in the data? b. Create a linear trend equation for this time series in Excel or Minitab. c. Create a quadratic trend equation for this time series in Excel or Minitab. d. Compare each model's MSE. According to MSE, which model appears to be superior? e. Forecast revenue for the tenth quarter using the models developed in parts (b) and (c). f. Which of the two forecasts in part (e) do you prefer? Explain.

The values of Alabama building contracts (in $millions) for a 12-month period follow.$

$$\begin{matrix} \text{240} & \text{350} & \text{230} & \text{260} & \text{280} & \text{320} & \text{220} & \text{310} & \text{240} & \text{310} & \text{240} & \text{230}\\ \end{matrix}$$

$a. Construct a time series plot. What type of pattern exists in the data? b. Compare the three-month moving average approach with the exponential smoothing forecast using$\alpha =$ .2. Which provides more accurate forecasts based on MSE? c. What is the forecast for the next month?

The values of Alabama building contracts (in millions of dollars) for a 12-month period follow:

$$\begin{array}{llllllllllll} 240 & 350 & 230 & 260 & 280 & 320 & 220 & 310 & 240 & 310 & 240 & 230 \end{array}$$

Construct a time series plot. What type of pattern exists in the data?

The values of Alabama building contracts (in millions of dollars) for a 12-month period follow:

$$\begin{array}{llllllllllll} 240 & 350 & 230 & 260 & 280 & 320 & 220 & 310 & 240 & 310 & 240 & 230 \end{array}$$

Compare a three-month moving average forecast with an exponential smoothing forecast. Use $\alpha=0.2$. Which provides the better forecasts based on MSE?

The values of Alabama building contracts (in millions of dollars) for a 12-month period follow:

$$\begin{array}{llllllllllll} 240 & 350 & 230 & 260 & 280 & 320 & 220 & 310 & 240 & 310 & 240 & 230 \end{array}$$

What is the forecast for the next month using exponential smoothing with $\alpha=0.2$ ?