4.8 Fitting exponential models to data  (Page 7/12)

What might a scatterplot of data points look like if it were best described by a logarithmic model?

What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?

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

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

$y=2.104{\left(1.479\right)}^x$

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

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

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

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

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

A logistic model is given by the equation $P(t)=\frac{90}{1+5e^{-0.42t}}.$ 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?

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

What was the initial population of koi?

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

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

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

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

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

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

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

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

Use a graphing calculator to create a scatter diagram of the data.

Use the regression feature to find an exponential function that best fits the data in the table.

Write the exponential function as an exponential equation with base $e.$

Graph the exponential equation on the scatter diagram.

Use the intersect feature to find the value of $x$ for which $f(x)=4000.$

Use a graphing calculator to create a scatter diagram of the data.