91Ó°ÊÓ

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

Find \(N, A\), and \(b\), give a technology formula for the given function, and use technology to sketch its graph for the given range of values of \(x\). $$ k(x)=\frac{17}{2+6.5\left(1.05^{-x}\right)} ; \quad[0,100] $$

Sketch the graphs of the quadratic functions, indicating the coordinates of the vertex, the y-intercept, and the \(x\) -intercepts (if any). $$ f(x)=x^{2}+\sqrt{2} x+1 $$

Use logarithms to solve the given equation. (Round answers to four decimal places.) $$ 4.16 e^{x}=2 $$

Use technology to find the quadratic regression curve through the given points. (Round all coefficients to four decimal places.) $$ \\{(-1,2),(-3,5),(-4,3)\\} $$

Find the associated exponential decay or growth model. $$ Q=2,000 \text { when } t=0 ; \text { half-life }=5 $$

Use technology to find a logistic regression curve \(y=\frac{N}{1+A b^{-x}}\) approximating the given data. Draw a graph showing the data points and regression curve. (Roumd \(b\) to three significant digits and \(A\) and \(N\) to two significant digits.) $$ \begin{array}{|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & 0 & 30 & 60 & 90 & 120 & 150 \\ \hline \boldsymbol{y} & 30.1 & 20 & 12 & 7.2 & 3.8 & 2.4 \\ \hline \end{array} $$

Find the associated exponential decay or growth model. $$ Q=1,000 \text { when } t=0 ; \text { doubling time }=2 $$

Find the associated exponential decay or growth model. $$ Q=2,000 \text { when } t=0 ; \text { doubling time }=5 $$

The fuel efficiency (in miles per gallon) of an SUV depends on its weight according to the formula \(^{4}\) $$ E=0.0000016 x^{2}-0.016 x+54 \quad(1,800 \leq x \leq 5,400) $$ where \(x\) is the weight of an SUV in pounds. According to the model, what is the weight of the least fuel-efficient SUV? Would you trust the model for weights greater than the answer you obtained? Explain.