Expert Answers to Algebra 2 Problems

Involve rational functions that model the given situations. In each case, find the horizontal asymptote as ${\displaystyle x\to \infty }$ and then describe what this means in practical terms.
${\displaystyle f\left(x\right)=\frac{150x+120}{0.05x+1}}$ the number of bass. f(x), months in a lake that was stocked with 120 bass.

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.

$\begin{array}{|cccccc|}\hline x& -1& 0& 1& 2& 3\\ g(x)& 2& 5& 8& 11& 14\\ \hline\end{array}$

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.

$\begin{array}{cc}\text{x}& \text{f(x)}\\ \text{-1,-1}& \text{32, 23}\\ \text{0}& \text{3}\\ \text{1}& \text{6}\\ \text{2}& \text{12}\\ \text{3}& \text{24}\end{array}$

Use the factors to identify the zeros of $f(x)=3x^3+12x^2-36x$. Then sketch the graph of the polynomial.

For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain. $y=220(1.06{)}^x$

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at $x=-5$, $x=-2$, and $x=1$. y-intercept at (0, 6)

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 4. Root of multiplicity 2 at $x=4,$ and roots of multiplicity 1 at $x=1$ and $x=minus$;2. y-intercept at (0, minus;3).

Investigate asymptotes of rational functions. Copy and complete the table. Determine the horizontal asymptote of each function algebraically. Function Horizontal Asymptote
${\displaystyle f\left(x\right)=\frac{x^2-5x4}{x^3+2}}$
${\displaystyle h\left(x\right)=\frac{x^3-3x^2+4x-12}{x^4-4}}$
${\displaystyle g\left(x\right)=\frac{x^4-1}{x^5+3}}$

India is currently one of the world’s fastest-growing countries. By 2040, the population of India will be larger than the population of China; by 2050, nearly one-third of the world’s population will live in these two countries alone. The exponential function ${\displaystyle f\left(x\right)=574{\left(1.026\right)}^x}$ models the population of India, f(x), in millions, x years after 1974. Find India’s population, to the nearest million, in the year 2055 as predicted by this function.

Write and solve an equation to determine the width w of the flag $[9.5ft]$
The length of an American flat is $1.9\times$ its width Equation $=9.5$
The width of the flag is feet.

Are these two lines parallel, perpendicular, the same line, or none of these?

$-3x=3y+6$
$4x+4y=2$
a) perpendicular
b) the same line
c) parallel
d) none of these

Use substitution to convert the integrals to integrals of rational functions. Then use partial fractions to evaluate the integrals.
${\displaystyle \int \frac{1}{2+e^{-x}}dx}$