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

Suppose that the functions \( f \) and \( g \) are defined as follows. \[ \begin{array}{l}f(x)=2 x+3 \\ g(x)=\sqrt{4 x+1} \\ \text { Find } \frac{f}{g} \text { and } f-g \text {. Then, give their domains using interval notation. } \\ \begin{array}{l}\left(\frac{f}{g}\right)(x)=\square \\ \text { Domain of } \frac{f}{g}: \square \\ \text { Domain of } f-g: \square\end{array} \\ \qquad\end{array} \] \( \begin{array}{l}\qquad-g)=\square\end{array} \) \[ \]

Consider the following. \[ f(x)=\frac{3 x^{2}-19 x+20}{3 x^{2}-x-70} \] (a) State the domain of the function. all real numbers \( x \) except \( x=\frac{4}{3}, 5 \) all real numbers \( x \) except \( x=-\frac{5}{3}, 14 \) all real numbers \( x \) except \( x=-\frac{14}{3}, 5 \) all real numbers \( x \) except \( x=-5, \frac{14}{3} \) Identify all intercepts; (If an answer does not exist, enter DNE.) \( x \)-intercept \( \quad(x, y)=(\square \)-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.

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