Algebra Word Problem Solutions

18 is 9% of what number?

The close connection between logarithm and exponential functions is used often by statisticians as they analyze patterns in data where the numbers range from very small to very large values. For example, the following table shows values that might occur as a bacteria population grows according to the exponential function P(t)=50(2t):
Time t (in hours)012345678 Population P(t)501002004008001,6003,2006,40012,800
a. Complete another row of the table with values log (population) and identify the familiar function pattern illustrated by values in that row.
b. Use your calculator to find log 2 and see how that value relates to the pattern you found in the log P(t) row of the data table.
c. Suppose that you had a different set of experimental data that you suspected was an example of exponential growth or decay, and you produced a similar “third row” with values equal to the logarithms of the population data.
How could you use the pattern in that “third row” to figure out the actual rule for the exponential growth or decay model?

A circle has parametric equations ${\displaystyle x=\sin t-5,y=\cos t+2}$
a.Find Cartesian equation of the circle
b.Write down the radius and the coordinates of the centre of the circle
c. Write down a suitable domain of t which defines one full revolution around the circle.

If you solve a work-rate problem and your solution, which represents the amount of time it would take working together, exceeds the individual working alone times that are given, then how do you know your solution is unreasonable? Explain.

The total revenue R (in dollars) is directly proportional to the number of units sold x. When 500 units are sold, the total revenue is $4825. Find a mathematical model that relates the total revenue R to the number of units sold x.

Identify the lines that are parallel.
Line 1: $y=-5$
Line 2: $4y-16x=-1$
Line 3: $x=-6$
Line 4: $y+5=4(x+1)$

Is $\frac{4}{\frac{6}{7}}=4$?

Chuck receives loans totaling $12,000 from two ba
. One bank charges 7.5% annual interest, and the second bank charges 6% annual interest. He paid $840 in total interest in one year. How much was loaned at each bank?

Desiree drove north for 30 minutes at 50 miles per hour. Then, she drove south for 60 minutes at 20 miles per hour. How far and in what direction is Desiree from where she started?

The equation ${\displaystyle m^{\frac{2}{3}}+10m^{\frac{1}{3}}+9=0}$ is said to be in __________form, because making the substitution u = __________results in a new equation that is quadratic.

Graph the solution set of the system of inequalities.
${\displaystyle x-y\le 2x-y\le 2}$
${\displaystyle x\ge 3}$

Draw the graph of inequalities
${\displaystyle \{\begin{array}{c}|x-2|\le 5\\ |y-4|>2\end{array}}$

Solve the polynomial inequality graphically. ${\displaystyle 3x^4-5x^3-12x^2+12x+16}$

Write the augmented matrix of the following system of equations.
${\displaystyle \{\begin{array}{c}8x+4y+2=0\\ 4x-8y-6=0\end{array}}$

1)${\displaystyle y=\{\begin{array}{cc}\sqrt{-x}& -4\le x\le 0\\ \sqrt{x}& 0<x\le 4\end{array}}$
2)${\displaystyle y=\{\begin{array}{cc}-x-2& -2\le x\le -1\\ x& -1<x\le 1\\ -x+2& 1<x\le 2\end{array}}$
Piecewise-Defined Functions. Find the (a) domain and (b) range.

Given a homogeneous system of linear equations, if the system is overdetermined, what are the possibilities as to the number of solutions?
Explain.

Determine whether the equation represents y as a function of x. x+y2=3x+y
2
=3

Write each radical expression using exponents and each exponential expression using radicals.
$\frac{RadicalexpressionExponentialexpression}{\sqrt[5]{5^3}}$