Algebra Word Problem Solutions

Solve the following equations and inequalities for x.
${\displaystyle 2(x-3)>4}$

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.

Describe mathematical modeling in you r own words.

Explain how to determine whether an exponential model of the form ${\displaystyle y=C{e}^{k}t}$ models growth or decay.

Tell whether the function represents exponential growth or exponential decay. Explain.
${\displaystyle y=2{\left(2.1\right)}^x}$

Find the multiplier for the rate of exponential growth or decay. 0.4% growth _______

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

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.

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

True or False. Some rational functions have holes in their graph.

Determine whether each function is an example of exponential growth or decay. Then find the y-intercept. ${\displaystyle y=\frac{7}{8}{\left(18\right)}^x}$

Identify the function as exponential growth or exponential decay.Then identify the growth or decay factor.
${\displaystyle y=1.3{\left(\frac{1}{4}\right)}^x}$

To find the equation $h+9.7=-9.7$

Explain the difference between the graphs of polynomial functions with a degree of 3 that have a positive leading coefficient and the graphs of those with a negative leading coefficient.

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

${\displaystyle \frac{3}{4}-\left(\frac{3}{5}\right)x=\left(\frac{2}{5}\right)x+\frac{2}{4}}$

Contain linear equations with constants in denominators. Solve each equation. ${\displaystyle 20-\left(\frac{x}{3}\right)=\frac{x}{2}}$

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.

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

How does one find the lovely asymptotes of a polynomial graph?

If the richest 5% includes 5.85 million households, how many households, in millions, are there in the United States?

${\displaystyle y=3+\sqrt{y^2-5}}$