# Recent questions in Algebra II

Complex numbers

### An $$8\times8$$ chessboard has a square cell (or box, like square a1) which measures $$\beta$$ inches on one side. Express the two possible moves of your knight in vector form with units in inches. What are the distances of each possible move from your original position in inches? What are their angles from the horizontal (x-axis)?

Exponential growth and decay

### Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. $$f(t)=6(0.84)^t$$

Exponential models

### Sociologists have found that information spreads among a population at an exponential rate. Suppose that the function $$y=525(1−e^{−0.038t})$$ models the number of people in a town of 525 people who have heard news within t hours of its distribution. How many people will have heard about the opening of a new grocery store within 24 hours of the announcement?

Exponential growth and decay

### Without graphing, determine whether the function $$y = 0.3(1.25)x$$ represents exponential growth or decay. State how you made the determination.

Exponential growth and decay

### Determine whether the function $$\displaystyle{y}={156}{\left({0.825}\right)}^{{t}}$$ represents exponential growth, exponential decay, or neither. Explain

Rational functions

### Given the domain of the rational functions. Write your answers in set notation and interval notation.

Rational functions

### For the following exercises, find the domain of the rational functions. $$\displaystyle{f{{\left({x}\right)}}}=\frac{{{x}-{1}}}{{{x}+{2}}}$$

Exponential models

### Find the mean of the data. 9,12,11,11,10,7,4,8

Exponential models

Modeling

Complex numbers

### The variable z is often used to denote a complex number and z¯ is used to denote its conjugate. If z = a+bi, simplify the expression $$\displaystyle{z}^{{{2}}}-\overline{{{z}}}^{{{2}}}$$

Rational functions

Modeling

Modeling

### Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. To earn an A in a course, you must have a final average of at least 90%. On the first four examinations, you have grades of 86%, 88%, 92%, and 84%. If the final examination counts as two grades, what must you get on the final to earn an A in the course?

Rational functions

Modeling

### There is a news clipping from Scientific American on modeling global climatic change. Without doing research, discuss how this might be accomplished.

Exponential models

Modeling

### Marilda has a block of modeling clay that is 8 inches by 5 inches by 3 inches. She is experimenting with different shapes that can be made from the clay. Give your answers to the nearest tenth. What size could could she make from the clay?

Rational functions