# Look at this table:x y1–22–43–84–165–32Write a linear (y=mx+b),

Question
Functions

Look at this table:

$$\begin{array}{|c|c|}\hline x & y \\ \hline 1 & 2 \\ \hline 2 & 4 \\ \hline 3 & 8 \\ \hline 4 & 16 \\ \hline 5 & 32 \\ \hline \end{array}$$

Write a linear $$(y=mx+b),$$ quadratic $$(y=ax2)$$, or exponential $$(y=a(b)x)$$ function that models the data.

$$y=?$$

2020-11-28
The x-values are increasing by 1 each time and the y-values are doubling each time. Since the y-values are increasing by a constant factor of 2, the model must be exponential. The data would have to increase by a constant amount to be linear and the second difference of the y-values would have to be constant for the model to be quadratic.
Notice that each yy-coordinate is a power of 2. Since $$\displaystyle{2}={2}^{{1}},{4}={2}^{{2}},{8}={2}^{{3}},{16}={2}^{{4}}$$, and $$\displaystyle{32}={2}^{{5}}$$, then each y-coordinate is a power of 2 where the exponent is the x-coordinate. The equation is then $$\displaystyle{y}={2}^{{x}}$$.

### Relevant Questions

For the expression: $$y = 4x – 2$$, complete the following table: X: 1 3 6 10 Y:

Which of the following is an equation of the line that has a y-intercept of 2 and an x-intercept of 3?
(a) $$-2x + 3y = 4$$
(b) $$-2x + 3y = 6$$
(c) $$2x + 3y = 4$$
(d) $$2x + 3y = 6$$
(e) $$3x + 2y = 6$$

Evaluate the piecewise defined function at the indicated values.
$$a^m inH$$
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$$a^m inH$$
f(-3),f(0),f(2),f(3),f(5)

What is the slope of a line perpendicular to the line whose equation is $$x - y = 5$$. Fully reduce your answer.

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Determine if each relationship is an additive relationship. Explain. Input (x) Output (y) 4 5 7 9 10 13 ​

Find (f o g)(x) and (g o f)(x), if
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find the values of b such that the function has the given maximum or minimum value. $$f(x) = -x^2+bx-75$$, Maximum value: 25

A surface is represented by the following multivariable function,
$$\displaystyle{f{{\left({x},{y}\right)}}}=\frac{{1}}{{3}}{x}^{{3}}+{y}^{{2}}-{2}{x}{y}-{6}{x}-{3}{y}+{4}$$
a) Calculate $$\displaystyle{f}_{{x x}},{f}_{{{y}{x}}},{f}_{{{x}{y}}}{\quad\text{and}\quad}{f}_{{{y}{y}}}$$
b) Calculate coordinates of stationary points.
c) Classify all stationary points.

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.