Chapter 9: Chapter 9

Vour other local banker tells you that the reason her bank doesn't offer continuously compounded interest is that it is equivalent to offering a fractionally higher interest rate compounded daily. Comment on her reasoning.

For each demand equation, express the total revenue \(R\) as a function of the price \(p\) per item, sketch the graph of the resulting function, and determine the price \(p\) that maximizes total revenue in each case. $$ q=-4 p+100 $$

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.] $$ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & & \\ \hline \end{array} $$ \(s(x)=2^{x-1}\)

Use logarithms to solve the given equation. (Round answers to four decimal places.) $$ 5\left(1.06^{2 x+1}\right)=11 $$

For each demand equation, express the total revenue \(R\) as a function of the price \(p\) per item, sketch the graph of the resulting function, and determine the price \(p\) that maximizes total revenue in each case. $$ q=-3 p+300 $$

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.] $$ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & & \\ \hline \end{array} $$ \(s(x)=2^{1-x}\)

Use logarithms to solve the given equation. (Round answers to four decimal places.) $$ 4\left(1.5^{2 x-1}\right)=8 $$

For each demand equation, express the total revenue \(R\) as a function of the price \(p\) per item, sketch the graph of the resulting function, and determine the price \(p\) that maximizes total revenue in each case. $$ q=-2 p+400 $$

Graph the given function. $$ f(x)=\log _{4} x $$

Using a chart of values, graph each of the functions .\( (Use \)-3 \leq x \leq 3 .)$ \(f(x)=3^{-x}\)