Chapter 7 Test: Algebra

Front

What is a linear function?

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

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

How do you convert a number to exponential form?

Back

To convert a number to exponential form, express it as a product of a base raised to an exponent, e.g., 8 can be written as 2^3.

Front

What is the decay factor if the decay rate is 23%?

Back

The decay factor is 0.77, calculated as 1 - 0.23.

Front

How do you find the number of insects after a certain number of years if the population doubles each year?

Back

Use the formula f(x) = initial population * 2^x. For example, if the initial population is 1600, after 3 years, f(3) = 1600 * 2^3 = 12800.

Front

What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the value of y when x = 0; it is the point where the line crosses the y-axis.

Front

What does it mean for a function to be neither linear nor exponential?

Back

A function is neither linear nor exponential if it does not fit the characteristics of a straight line or an exponential curve, such as quadratic or logarithmic functions.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.