Algebra Word Problem Solutions

The exponential models the population of the indicated country, A, in millions, t years after 20006. Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
Country 1: $A=26.3e^{0.029t}$
Country 2: $A=127.7e^{0.007t}$
Country 3: $A=148.5e^{-0.0091t}$
Country 4: $A=1094.2e^{0.016t}$

Solve for the value of x upto correct decimal approximation ${\displaystyle \log (x+6)=\log (3x-2)+2}$
Solving this equation will determine the x-cordinate of the point of intersection of the function ${\displaystyle y=\log x(x+6)\text{and}y=\log (3x-2)+2)}$

how do you graph y > -2

The ratio 216:x is equivalent to the ratio ${\displaystyle x^2:216}$. What is the value of x?

HOW DO I SOLVE THIS EQUATION -11+Z=7

Use Vietas

How do you calculate the following retaining the correct number of significant figures ${\displaystyle 12.432\times 3=}$ and ${\displaystyle 208\times 62.1=}$

Sketch the graph of the solution of the system of linear inequlities
-3x+2y<6
x+4y>-2
2x+y<3

Graph each polynomial function. ${\displaystyle f\left(x\right)=2x^3-7x^2+2x+3}$ given that 3 is a zero.

Gven ${\displaystyle f\left(x\right)=3x-2\text{and}g\left(x\right)=\frac{1}{3}x+\frac{2}{3}}$
Find ${\displaystyle \left(fog\right)\left(x\right)}$

Whether the division of polynomial $\frac{3x^4-x+1}{x-5}$ using synthetic division method is directly possible or not.

Find the solution of the equation rounded to two decimals. ${\displaystyle \frac{1.73x}{2.12+x}=1.51}$

What is the absolute value function?

Give an example of Piecewise-Defined Functions?

Use Cramer’s Rule to solve (if possible) the system of linear equations.
4x-y-z=1
2x+2y+3z=10
5x-2y-2z=-1

The value of a home y (in thousands of dollars) can be approximated by the model, $y=192(0.96{)}^t$ where t is the number of years since 2010.
1. The model for the value of a home represents exponential _____. (Enter growth or decay in the blank.)
2. The annual percent increase or decrease in the value of the home is ______ %. (Enter the correct number in the blank.)
3. The value of the home will be approximately $161,000 in the year

Rewrite each expression so that each term is in the form $k{x}^n,$ where k is a real number, x is a positive real number, and n is a rational number.
a)$x^{-\frac{2}{3}}\times x^{\frac{1}{3}}=?$
b) $\frac{10x^{\frac{1}{3}}}{2x^2}=?$
c) $(3x^{\frac{1}{4}}{)}^{-2}=?$

A population of 6 mice doubles every 4 weeks. When will this population reach 120 mice? Use an algebraic solving process.

Twenty-one independent measurements were taken of the hardness (on the Rockwell C scale) of HSLA-100 steel base metal, and another 21 independent measurements were made of the hardness of a weld produced on this base metal.
The standard deviation of the measurements made on the base metal was 3.06, and the standard deviation of the measurements made on the weld was 1.41.
Assume that the measurements are independent random samples from normal populations.
Need to conclude that measurements made on the base metal are more variable than measurements made on the weld?