123. Sheep population. A herd of sheep doubles in size every three years. There are now 1500 sheep in the herd. a. Find an exponential function of the form \( P=P_{0} e^{r t} \) to model the herd's growth. b. How many sheep will be in the herd seven years from now (round your answer)? c. In how many years will the herd have 15,000 sheep?

The number of bacteria growing in an incubation culture increases with time according to \( B(x)=9,900(5)^{x} \), where \( x \) is time in days. Find the number of bacteria when \( x=0 \) and \( x=4 \). A. \( 9,900,30,937,500 \) B. \( 49,500,6,187,500 \) C. \( 9,900,6,187,500 \) D. \( 9,900,198,000 \)

Unit 3 AsSessment Path of Lava Lava coming from the eruption of a volcano follows a parabolic path. The height \( h \) in feet of a piece of lava \( t \) seconds after it is ejected from the volcano is given by \( h(t)=-t^{2}+16 t+936 \).

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 \( \quad(x, y)=(\square) \)

Score on last try: 0.5 of 1 pts. See Details for more. A computer purchased for \( \$ 1,400 \) loses \( 17 \% \) of its value every year. The computer's value can be modeled by the function \( v(t)=a \cdot b^{t} \), where \( v \) is the dollar value and \( t \) the number of years since purchase. (A) Give the function that models the decrease in value of the computer: \( v(t)= \) \( 1400 \cdot(0.83)^{t} \) (B) In how many years will the computer be worth half its original value? Round answer to 1 decimal place. \( 3.72 \quad \times \) years

Consider the following. \[ \begin{array}{l}P(x)=\frac{1-5 x}{1-x} \\ \text { (a) State the domain of the function. } \\ \text { all real numbers } x \text { except } x=\frac{1}{5} \\ \text { all real numbers } x \text { except } x=-\frac{1}{5} \\ \text { all real numbers } x \text { except } x=-1 \\ \text { all real numbers } x\end{array} \] all real numbers \( x \) except \( x=1 \)