Algebra Word Problem Solutions

Suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive. What is the probability that the number will be more than 4 or odd?

Tell whether each function represents exponential growth, exponential decay, or neither. Justify your responses.

$\begin{array}{|ccccc|}\hline x& 0& 2& 4& 6\\ y& 1& 9& 81& 729\\ \hline\end{array}$

Determine whether each function is an example of exponential growth or decay. Then, find the y-intercept. $y=25/7(7/5{)}^x$

Examine whether the series $\sum _1^{\infty }=(\log n{)}^{\log n}$ is convergent.

${\displaystyle n=2}$

The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with $t=9$ corresponding to 1999.

$\begin{array}{|lc|}\hline \text{ Year }& \text{ Population, }P\\ 1999& 427.4\\ 2000& 433.6\\ 2001& 439.0\\ 2002& 444.1\\ 2003& 448.3\\ 2004& 455.0\\ 2005& 461.2\\ 2006& 469.1\\ 2007& 476.2\\ 2008& 483.8\\ 2009& 493.5\\ 2010& 502.1\\ 2011& 511.8\\ 2012& 524.9\\ 2013& 537.0\\ \hline\end{array}$

(a) Use the regression feature of a graphing utility to find a linear model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (b) Use the regression feature of the graphing utility to find a power model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (c) Use the regression feature of the graphing utility to find an exponential model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (d) Use the regression feature of the graphing utility to find a logarithmic model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (e) Which model is the best fit for the data? Explain. (f) Use each model to predict the populations of Luxembourg for the years 2014 through 2018. (g) Which model is the best choice for predicting the future population of Luxembourg? Explain. (h) Were your choices of models the same for parts (e) and (g)? If not, explain why your choices were different.

Write $y=13x+7$ in standard form using integers.

a. $-2x+3y=21$

b. $3x-2y=21$

c. $-2x-3y=21$

Determine whether a linear, quadratic, or exponential function best models the data. Then, use regression to find the function that models the data. 

$\begin{array}{|cccccc|}\hline x& 0& 1& 2& 3& 4\\ y& 100& 89.5& 78.9& 68.4& 57.8\\ \hline\end{array}$

use long division to determine if $2x-1$ is a factor of ${\displaystyle p\left(x\right)=6x^3+7x^2-x-2}$

During a test by the editors of an auto magazine, the stopping distance s (in metres) of the MacPherson X-2 racing car conformed to the rule
${\displaystyle s=f\left(t\right)=40t-5t2(t\ge 0)}$ where t was the time (in seconds) after the brakes were applied.
a. Find an expression for the car's velocity v at any time t.
b. What was the car's velocity when the brakes were first applied?
c. What was the car's stopping distance for that particular test? Hint: The stopping time is found by setting v=0.