Master Algebra 1 Word Problems with our Comprehensive Practice

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.

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.

What would be the linear equation for this function, and the graph?
${\displaystyle (X_1,Y_1)=(4,8),(X_2,Y_2)=(6,-9)}$

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.

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

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?

An automobile saleswoman earns 12% on all of her sales. Last month she sold 3 cars for a total sales amount of $28,950. What is her commission?

solve ${\displaystyle x^2-10x=-21x}$

According to the U.S. Bureau of Labor Statistics, you will devote 37 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 19. Over your lifetime, how many years will you spend each of these activities?

A water sample in a laboratory initially contains 6000 bacteria. The organisms reproduce at a rate of 10% per hour. Find the function that corresponds to this situation. Then predict how long it will take for the population of bacteria to double in number. Round your answer to the nearest hundredth of an hour.

${\displaystyle 36n^2+102n-84}$

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

in order to write an exponential growth equation in the form ${\displaystyle y=a{\left(b\right)}^x}$, you first take the initial value and do what?

Graph the solution set of the system of inequalities or indicate that the system has no solution.
${\displaystyle \{\begin{array}{c}x+y>4\\ x+y<-1\end{array}}$

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
${\displaystyle \{\begin{array}{c}|x-2|\le 5\\ |y-4|>2\end{array}}$

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.

What is a system of linear equations in three variables?