Once approved by the U. S. Patent and Trademark Office, a patent can last forever.

Write an equation that models the amount of money in Hannah’s account after x years. (Hint: I recommend using ^ for exponents and / for fractions, if needed.)

Using the graph, which function should have the least value for b? Explain your thinking.

State the value of f (12), and write a sentence explaining what this input and its output mean in terms of this problem. Use numbers and units (blocks & array number) in your sentence.

Which daughter will have more money in her college savings fund when she turns 18? (Hint: The evidence for your claim should be visible on the table if you chose good inputs for which you can easily find the outputs without a calculator.)

0 < log(.01) < 1

The molar concentration of hydrogen ions of a substance is .000000001. The pH of the substance is: Hint: pH = -log (Molar Concentration of Hydrogen Ions)

Define an equation for the Area, f(x), as a function of the length, x, of one side of the garden described in the previous question.

log (100 ÷ 1000) = log(100) – log(1000)

Write an equation for f(x) in the form of y= (a)⋅(b)x. Next, use a point, other than the y-intercept, that is unique to your graph to show your equation works. [This work can be submitted on scratch paper, if needed, after the exam. Be sure to state which question it came from.]