Kristen K.

For the following exercises, use this scenario: The population $P$ of an endangered species habitat for wolves is modeled by the function $P(x)=\frac{558}{1+54.8 e^{-0.42 x}},$ 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.

For the following exercises, refer to Table 7.
$$\begin{array}{ccccccc}{x} & {1} & {2} & {3} & {4} & {5} & {6} \\ {f(x)} & {1125} & {1495} & {2310} & {3294} & {4650} & {6361}\end{array}$$

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

For the following exercises, refer to Table 7.
$$\begin{array}{ccccccc}{x} & {1} & {2} & {3} & {4} & {5} & {6} \\ {f(x)} & {1125} & {1495} & {2310} & {3294} & {4650} & {6361}\end{array}$$

Graph the exponential equation on the scatter diagram.

For the following exercises, refer to Table 8.
$$\begin{array}{ccccccc}{x} & {1} & {2} & {3} & {4} & {5} & {6} \\ {f(x)} & {555} & {383} & {307} & {210} & {158} & {122}\end{array}$$

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

For the following exercises, refer to Table 8.
$$\begin{array}{ccccccc}{x} & {1} & {2} & {3} & {4} & {5} & {6} \\ {f(x)} & {555} & {383} & {307} & {210} & {158} & {122}\end{array}$$

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

For the following exercises, refer to Table 8.
$$\begin{array}{ccccccc}{x} & {1} & {2} & {3} & {4} & {5} & {6} \\ {f(x)} & {555} & {383} & {307} & {210} & {158} & {122}\end{array}$$

Use the intersect feature to find the value of $x$ for which $f(x)=250$ .