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The following table shows Apple iPhone sales from the 2nd quarter in 2007 through the second quarter in \(2008(t=2\) represents the second quarter of 2007\():^{.11}\) $$ \begin{array}{|r|c|c|c|c|c|} \hline \text { Quarter } \boldsymbol{t} & 2 & 3 & 4 & 5 & 6 \\ \hline \begin{array}{r} \text { iPhone Sales } \\ \text { (thousands) } \end{array} & 270 & 1,119 & 2,315 & 1,703 & 717 \\ \hline \end{array} $$ a. Find a quadratic regression model for these data. (Round coefficients to the nearest whole number.) Graph the model together with the data. b. What does the model predict for iPhone sales in the third quarter of \(2008(t=7)\) to the nearest 1,000 units? Comment on the answer, and ascertain the actual third quarter sales in 2008 ( Apple's fiscal fourth quarter).

On the same set of axes, use technology to graph the pairs of functions with \(-3 \leq x \leq 3 .\) Identify which graph corresponds to which function. HINT [See Quick Examples on page 634.] \(f_{1}(x)=1.6^{x}, f_{2}(x)=1.8^{x}\)

Suppose the graph of revenue as a function of unit price is a parabola that is concave down. What is the significance of the coordinates of the vertex, the \(x\) -intercepts, and the \(y\) -intercept?

Suppose the height of a stone thrown vertically upward is given by a quadratic function of time. What is the significance of the coordinates of the vertex, the (possible) \(x\) -intercepts, and the \(y\) -intercept?

Is a quadratic model useful for long-term prediction of sales of an item? Why?

The rate of auto thefts triples every 6 months. a. Determine, to two decimal places, the base \(b\) for an exponential model \(y=A b^{t}\) of the rate of auto thefts as a function of time in months. b. Find the doubling time to the nearest tenth of a month.

The rate of television thefts is doubling every 4 months. a. Determine, to two decimal places, the base \(b\) for an exponential model \(y=A b^{t}\) of the rate of television thefts as a function of time in months. b. Find the tripling time to the nearest tenth of a month.

Explain why, if demand is a linear function of unit price \(p\) (with negative slope), then there must be a single value of \(p\) that results in the maximum revenue.

The half-life of strontium 90 is 28 years. a. Obtain an exponential decay model for strontium 90 in the form \(Q(t)=Q_{0} e^{-k t} .\) (Round coefficients to three significant digits.) b. Use your model to predict, to the nearest year, the time it takes three- fifths of a sample of strontium 90 to decay.

Soon after taking an aspirin, a patient has absorbed \(300 \mathrm{mg}\) of the drug. If the amount of aspirin in the bloodstream decays exponentially, with half being removed every 2 hours, find, to the nearest \(0.1\) hour, the time it will take for the amount of aspirin in the bloodstream to decrease to \(100 \mathrm{mg}\).