91Ó°ÊÓ

Model the data using an exponential function \(f(x)=A b^{x} .\) HINT [See Example 1.] $$ \begin{array}{|c|c|c|c|} \hline x & 0 & 1 & 2 \\ \hline f(x) & 500 & 225 & 101.25 \\ \hline \end{array} $$

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.

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

Model the data using an exponential function \(f(x)=A b^{x} .\) HINT [See Example 1.] $$ \begin{array}{|c|c|c|c|} \hline x & 0 & 1 & 2 \\ \hline f(x) & 5 & 3 & 1.8 \\ \hline \end{array} $$

Of what use is a quadratic model, if not for long-term prediction?

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.

Model the data using an exponential function \(f(x)=A b^{x} .\) HINT [See Example 1.] $$ \begin{array}{|c|c|c|} \hline \boldsymbol{x} & 1 & 2 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & -110 & -121 \\ \hline \end{array} $$

The half-life of cobalt 60 is 5 years. a. Obtain an exponential decay model for cobalt 60 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 one third of a sample of cobalt 60 to decay.

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.

Model the data using an exponential function \(f(x)=A b^{x} .\) HINT [See Example 1.] $$ \begin{array}{|c|c|c|} \hline \boldsymbol{x} & 1 & 2 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & -41 & -42.025 \\ \hline \end{array} $$