How can you tell whether the graph of a function of form

$$f(x) = ab^x$$

will increase or decrease from left to right?

Write an exponential function for each set of points. a. (0, 3), (1, 12), (2, 48), (3, 192), and (4, 768) b. (0, 2, 187), (1, 729), (2, 243), (3, 81), and (4, 27)

Martin says that $f(x)=2(4)^{x}$ starts at 4 and has constant ratio of 2. What error did Martin make? Explain.

Use two pieces of $8\frac{1}{2}$ by 11 paper. Fold one of the pieces of paper accordion-style for five folds. Fold the other in half for five folds. After each fold, unfold each piece of paper and count the total number of rectangular sections. Explain why the two different folded pieces of paper produce different results.

How long will it take for the virus to spread to 50,000 computers?

What are the properties of rational exponents and how are they used to solve problems?

Identify the key features of the function $f(x)=b^x$ for b=2 and $b=\frac{1}{2}$.

When is using a graph to solve a system of equations more useful than the substitution method?

Juanita is painting her house. She can either buy Brand A paint and a paint roller tray or Brand B paint and a grid for the paint roller. For how many gallons of paint would the price for both options be the same? If Juanita needs 15 gallons of paint, which is the better option? 1-gallon can (Brand A): $27/gallon 1 paint roller tray:$3 1-gallon can (Brand B): $25/gallon 1 grid for paint roller:$5

List four indicators that a chemical change has probably taken place.

Why is it important to recognize and analyze the various influences on your behavior?

A student claims that the inequality $y\lt1$ cannot be graphed on a coordinate grid since it has only one variable. Explain the error the student made.

Rikki says that the product $\sqrt{3 x^{3}} \cdot \sqrt{x}$ is $3 x^{2}$. Explain Rikki's error and write the correct product.

How are rational exponents different than whole number exponents? How are they the same?