지수함수와 로그함수 전체 문제

For the following exercises, match the given function of best fit with the appropriate scatterplot in (the referenced figure) through (the referenced figure). Answer using the letter beneath the matching graph.

$y=10.209{e}^{-0.294x}$

For the following exercises, match the given function of best fit with the appropriate scatterplot in (the referenced figure) through (the referenced figure). Answer using the letter beneath the matching graph.

$y=5.598-1.912\ln (x)$

For the following exercises, match the given function of best fit with the appropriate scatterplot in (the referenced figure) through (the referenced figure). Answer using the letter beneath the matching graph.

$y=2.104{(1.479)}^{x}$

For the following exercises, match the given function of best fit with the appropriate scatterplot in (the referenced figure) through (the referenced figure). Answer using the letter beneath the matching graph.

$y=4.607+2.733\ln (x)$

For the following exercises, match the given function of best fit with the appropriate scatterplot in (the referenced figure) through (the referenced figure). Answer using the letter beneath the matching graph.

$y=\frac{14.005}{1+2.79{e}^{-0.812x}}$

To the nearest whole number, what is the initial value of a population modeled by the logistic equation $P(t)=\frac{175}{1+6.995{e}^{-0.68t}}?$ What is the carrying capacity?

Rewrite the exponential model $A(t)=1550{(1.085)}^{x}$ as an equivalent model with base $e.$ Express the exponent to four significant digits.

A logarithmic model is given by the equation $h(p)=67.682-5.792\ln (p).$ To the nearest hundredth, for what value of $p$ does $h(p)=62?$

A logistic model is given by the equation $P(t)=\frac{90}{1+5{e}^{-0.42t}}.$ To the nearest hundredth, for what value of t does $P(t)=45?$

What is the y-intercept on the graph of the logistic model given in the previous exercise?

For the following exercises, use this scenario: The population $P$ of a koi pond over $x$ months is modeled by the function $P(x)=\frac{68}{1+16{e}^{-0.28x}}.$

Graph the population model to show the population over a span of $3$ years.

For the following exercises, use this scenario: The population $P$ of a koi pond over $x$ months is modeled by the function $P(x)=\frac{68}{1+16{e}^{-0.28x}}.$

What was the initial population of koi?

For the following exercises, use this scenario: The population $P$ of a koi pond over $x$ months is modeled by the function $P(x)=\frac{68}{1+16{e}^{-0.28x}}.$

How many koi will the pond have after one and a half years?

For the following exercises, use this scenario: The population $P$ of a koi pond over $x$ months is modeled by the function $P(x)=\frac{68}{1+16{e}^{-0.28x}}.$

How many months will it take before there are $20$ koi in the pond?

For the following exercises, use this scenario: The population $P$ of a koi pond over $x$ months is modeled by the function $P(x)=\frac{68}{1+16{e}^{-0.28x}}.$

Use the intersect feature to approximate the number of months it will take before the population of the pond reaches half its carrying capacity.

For the following exercises, use this scenario: The population $P$ of an endangered species habitat for wolves is modeled by the function $P(x)=\frac{558}{1+54.8{e}^{-0.462x}},$ where $x$ is given in years.

Graph the population model to show the population over a span of $10$ years.

For the following exercises, use this scenario: The population $P$ of an endangered species habitat for wolves is modeled by the function $P(x)=\frac{558}{1+54.8{e}^{-0.462x}},$ where $x$ is given in years.

What was the initial population of wolves transported to the habitat?

For the following exercises, use this scenario: The population $P$ of an endangered species habitat for wolves is modeled by the function $P(x)=\frac{558}{1+54.8{e}^{-0.462x}},$ where $x$ is given in years.

How many wolves will the habitat have after $3$ years?

For the following exercises, use this scenario: The population $P$ of an endangered species habitat for wolves is modeled by the function $P(x)=\frac{558}{1+54.8{e}^{-0.462x}},$ where $x$ is given in years.

How many years will it take before there are $100$ wolves in the habitat?

For the following exercises, use this scenario: The population $P$ of an endangered species habitat for wolves is modeled by the function $P(x)=\frac{558}{1+54.8{e}^{-0.462x}},$ where $x$ is given in years.

Use the intersect feature to approximate the number of years it will take before the population of the habitat reaches half its carrying capacity.