지수함수와 로그함수 전체 문제

For the following exercises, refer to (the referenced table).

$x$	0	2	4	5	7	8	10	11	15	17
$f(x)$	12	28.6	52.8	70.3	99.9	112.5	125.8	127.9	135.1	135.9

Use the LOGISTIC regression option to find a logistic growth model of the form $y=\frac{c}{1+a{e}^{-bx}}$ that best fits the data in the table.

For the following exercises, refer to (the referenced table).

$x$	0	2	4	5	7	8	10	11	15	17
$f(x)$	12	28.6	52.8	70.3	99.9	112.5	125.8	127.9	135.1	135.9

Graph the logistic equation on the scatter diagram.

For the following exercises, refer to (the referenced table).

$x$	0	2	4	5	7	8	10	11	15	17
$f(x)$	12	28.6	52.8	70.3	99.9	112.5	125.8	127.9	135.1	135.9

To the nearest whole number, what is the predicted carrying capacity of the model?

For the following exercises, refer to (the referenced table).

$x$	0	2	4	5	7	8	10	11	15	17
$f(x)$	12	28.6	52.8	70.3	99.9	112.5	125.8	127.9	135.1	135.9

Use the intersect feature to find the value of $x$ for which the model reaches half its carrying capacity.

Use a graphing utility to find an exponential regression formula $f(x)$ and a logarithmic regression formula $g(x)$ for the points $(1.5,1.5)$ and $(8.5,\,8.5).$ Round all numbers to 6 decimal places. Graph the points and both formulas along with the line $y=x$ on the same axis. Make a conjecture about the relationship of the regression formulas.

Use the result from the previous exercise to graph the logistic model $P(t)=\frac{20}{1+4{e}^{-0.5t}}$ along with its inverse on the same axis. What are the intercepts and asymptotes of each function?

Determine whether (the referenced table) could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points.

Graph the function $f(x)=3.5{(2)}^{x}.$ State the domain and range and give the y-intercept.

Graph the function $f(x)=4{\left(\frac{1}{8}\right)}^{x}$ and its reflection about the y-axis on the same axes, and give the y-intercept.

The graph of $f(x)={6.5}^{x}$ is reflected about the y-axis and stretched vertically by a factor of $7.$ What is the equation of the new function, $g(x)?$ State its y-intercept, domain, and range.

The graph below shows transformations of the graph of $f(x)={2}^{x}.$ What is the equation for the transformation?

Graph the function $g(x)=\log (7x+21)-4.$

Graph the function $h(x)=2\ln (9-3x)+1.$

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic.

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic.

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic.

Find a formula for an exponential equation that goes through the points $(-2,100)$ and $(0,4).$ Then express the formula as an equivalent equation with base e.

For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.

For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.

For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.

Graph the function $f(x)=5{(0.5)}^{-x}$ and its reflection across the y-axis on the same axes, and give the y-intercept.