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)?

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

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?

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

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 \(\displaystyle{z}^{{{2}}}-\overline{{{z}}}^{{{2}}}\)

Show that an exponential model fits the data. Then write a recursive rule that models the data. \(\begin{array}{|c|c|}\hline n & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline f(n) & 162 & 54 & 18 & 6 & 2 & \frac{2}{3} \\ \hline \end{array}\)

Show that an exponential model fits the data. Then write a recursive rule that models the data.

\(\begin{array}{|c|c|} \hline n & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline f(n) & 2 & 6 & 18 & 54 & 162 & 486 \\ \hline \end{array}\)