Chapter 7 Review

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed.

Front

What does it mean for a function to be shifted down by 4 units?

Back

Shifting a function down by 4 units means that for every point (x, f(x)) on the graph of the function, the new point will be (x, f(x) - 4). This results in the entire graph moving downwards.

Front

What is the value of any number raised to the power of 0?

Back

Any non-zero number raised to the power of 0 is equal to 1. For example, 10^0 = 1.

Front

Back

Front

What is the principal amount in a compound interest problem?

Back

The principal amount is the initial sum of money that is invested or loaned, before interest is added.

Front

What does it mean for a function to be compared to a basic function?

Back

Comparing a function to a basic function involves analyzing how the new function is transformed from the basic function, such as shifts, stretches, or reflections.

Front

What is the significance of the base in an exponential function?

Back

The base in an exponential function determines the rate of growth or decay. For example, in f(x) = a^x, if a > 1, the function grows; if 0 < a < 1, the function decays.

Front

What is the formula for calculating the ending balance in compound interest?

Back

The ending balance can be calculated using the formula A = P(1 + r/n)^(nt), where A is the ending balance, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

Front

What does it mean for a function to be transformed vertically?

Back

A vertical transformation involves shifting the graph of the function up or down. For example, adding a constant to the function shifts it up, while subtracting a constant shifts it down.

Front

What is the relationship between exponential functions and their graphs?

Back

Exponential functions have graphs that are continuous and either increase or decrease rapidly, depending on the base. They never touch the x-axis.