Review Compound Interest, Direct Variation, and Functions

Front

What is compound interest?

Back

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Front

How do you calculate the future value of an investment with compound interest?

Back

The future value (FV) can be calculated using the formula: FV = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is a non-zero constant.

Front

How do you determine the constant of variation in a direct variation problem?

Back

The constant of variation (k) can be found by dividing the value of y by the value of x (k = y/x) when given a pair of values.

Front

What is the difference between direct variation and inverse variation?

Back

In direct variation, as one variable increases, the other variable also increases. In inverse variation, as one variable increases, the other variable decreases, expressed as xy = k.

Front

What does it mean for a relationship to be proportional?

Back

A relationship is proportional if two quantities maintain a constant ratio, meaning they can be expressed as y = kx for some constant k.

Front

How do you solve a system of equations graphically?

Back

To solve a system of equations graphically, plot both equations on the same graph and identify the point(s) where the lines intersect, which represents the solution(s) to the system.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, indicating the values of the variables that satisfy both equations simultaneously.

Front

How do you calculate the total amount after a certain number of years with compound interest?

Back

To calculate the total amount after a certain number of years, use the compound interest formula: A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, r is the interest rate, n is the number of compounding periods, and t is the time in years.

Front

What is the formula for calculating simple interest?

Back

Simple interest can be calculated using the formula: I = Prt, where I is the interest, P is the principal amount, r is the rate of interest per year, and t is the time in years.