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?

The cost in dollars to produce x youth baseball caps is \(\displaystyle{C}{\left({x}\right)}={4.3}{x}+{75}\). The revenue in dollars from sales of x caps is \(\displaystyle{R}{\left({x}\right)}={25}{x}\).
(a) Write and simplify a function P that gives profit in terms of x.
(b) Find the profit if 50 caps are produced and sold.

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

If f\((x) = x + 4\) and \(\displaystyle{g{{\left({x}\right)}}}={4}{x}²\), find \((f + g)(x)\ and\ (f + g)(2).\)