aCompute the missing values in the following table and supply a valid technology formula for the given function: HINT [See Quick Examples on page 633.] $$ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & & \\ \hline \end{array} $$ \(r(x)=2^{-x}+1\)

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?

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.

New York City Housing Costs: Uptown The following table shows the average price of a two-bedroom apartment in uptown New York City during the real estate boom from 1994 to \(2004 .^{25}\) $$ \begin{array}{|r|c|c|c|c|c|c|} \hline \boldsymbol{t} & 0(1994) & 2 & 4 & 6 & 8 & 10(2004) \\ \hline \begin{array}{r} \text { Price } \\ \text { (S million) } \end{array} & 0.18 & 0.18 & 0.19 & 0.2 & 0.35 & 0.4 \\ \hline \end{array} $$ a. Use exponential regression to model the price \(P(t)\) as a function of time \(t\) since 1994 . Include a sketch of the points and the regression curve. (Round the coefficients to 3 decimal places.) b. Extrapolate your model to estimate the cost of a twobedroom uptown apartment in 2005 .

I would like my investment to double in value every 3 years. At what rate of interest would I need to invest it, assuming the interest is compounded continuously? HIIII [See Duick Examnles nane 655.]

Convert the given exponential function to the form indicated. Round all coefficients to four significant digits. $$ f(t)=23.4(0.991)^{t} ; f(t)=Q_{0} e^{-k t} $$