NC.M1.F-BF Building Functions

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

How do you find the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence can be found using the formula: \( a_n = a_1 + (n-1)d \), where \( a_1 \) is the first term and \( d \) is the common difference.

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, \( r \) is the annual interest rate, \( n \) is the number of times that interest is compounded per year, and \( t \) is the number of years.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change and can be represented by the equation \( y = mx + b \). Exponential functions have a variable rate of change and can be represented by the equation \( y = ab^x \), where \( b \) is a constant.

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as \( f(x) \) where \( x \) is the input.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Front

How do you determine the slope of a line?

Back

The slope of a line is determined by the formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the line crosses the y-axis, represented by the value of \( b \) in the equation \( y = mx + b \).

Front

What is depreciation in financial terms?

Back

Depreciation is the reduction in the value of an asset over time, often due to wear and tear or obsolescence.

Front

What is the formula for the value of an asset after depreciation?

Back

The formula for the value of an asset after depreciation is: \( V(t) = V_0(1 - r)^t \), where \( V_0 \) is the initial value, \( r \) is the rate of depreciation, and \( t \) is the time in years.