V. The number of bacteria in a crop is represented by: \( f(t)=3(4)^{t} \), where \( t \) is measured in hours and \( f(t) \) in thousands. 1. What is the initial number of bacteria? 2. How many are they at 20 minutes? 3. How many are they in half an hour? 4. How many are they after \( 2 \frac{1}{2} \) hours?

Consider the following. \[ g(x)=\frac{x^{2}-2 x-35}{x^{2}-36} \] (a) State the domain of the function. (b) Identify all intercepts. (c) Find any vertical and horizontal asymptotes or holes. (d) Plot additional solution points as needed to sketch the graph of the rational function.

Consider the following. \[ \begin{array}{l}g(x)=\frac{5 x}{x^{2}+4 x-5} \\ \text { (a) State the domain of the function. } \\ \text { all real numbers } x \text { except } x=5 \\ \text { all real numbers } x \text { except } x=1 \\ \text { all real numbers } x \text { except } x=-5 \\ \text { all real numbers } x \text { except } x=-5 \text { and } x=1 \\ \text { (b) Identify all intercepts. (If an answer does not exist, enter DNE.) } \\ x \text { except } x=0 \\ x \text {-intercept } \quad(x, y)=(\square) \\ y \text {-intercept } \quad(x, y)=(\square)\end{array} \]

Consider the following. \[ \begin{array}{l}g(x)=\frac{6(x+3)}{x(x-6)} \\ \text { (a) State the domain of the function. } \\ \text { all real numbers } x \text { except } x=3 \text { and } x=6 \\ \text { all real numbers } x \text { except } x=0 \text { and } x=6 \\ 0 \text { all real numbers } x \text { except } x=-3 \text { and } x=6 \\ 0 \text { all real numbers } x \text { except } x=0 \text { and } x=3 \\ \text { all real numbers } x \\ \text { (b) Identify all intercepts. (If an answer does not exist, enter DNE.) } \\ x \text {-intercept } \quad(x, y)=(\square)\end{array} \] \( y \)-intercept \( \quad(x, y)=(\square) \)

Consider the following. \[ f(x)=\frac{x^{2}+4}{x+1} \] (a) State the domain of the function. (b) Identify all intercepts. (c) Find any vertical and slant asymptotes. (d) Plot additional solution points as needed to sketch the graph of the rational function.

Find an exponential function of the form \( P(t)=y_{0} e^{\mathrm{Kt}} \) to model the given data. In 1985, the number of female athletes participating in Summer Olympic-Type Games was 550. In 1996, about 3,650 participated in the Summer Olympics-Type games. Assuming that \( P(0)=550 \) and that the exponential model applies, find the value of \( k \) rounded to the hundredths place, and write the function. A. \( k=0.27 ; P(t)=550 e^{0.27 t} \) B. \( k=0.17 ; P(t)=550 e^{0.17 t} \) C. \( k=0.16 ; P(t)=550 e^{0.16 t} \) D. \( k=0.19 ; P(t)=550 e^{0.19 t} \)