ELD C/V: Final Review Algebra 1

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time. For example, if a population grows by 5% each year, it is experiencing exponential growth.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time. For example, if a radioactive substance loses 10% of its mass each year, it is experiencing exponential decay.

Front

Identify the exponential function: f(x) = 5 * (1/2)^x or f(x) = (1/2)x - 5

Back

f(x) = 5 * (1/2)^x is an exponential function because it has the form f(x) = a * b^x, where a is a constant and b is a base.

Front

Simplify: 2x * (-2x - 3)

Back

-4x^2 - 6x

Front

Find the difference: (3 - 2x + 2x^2) - (4x - 5 + 3x^2)

Back

-x^2 - 6x + 8

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where a is a constant, b is the base (b > 0, b ≠ 1), and x is the exponent.

Front

What does the base of an exponential function indicate?

Back

The base of an exponential function indicates the rate of growth or decay. If the base is greater than 1, the function represents growth; if the base is between 0 and 1, it represents decay.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, represented by a straight line, while exponential functions have a variable rate of change that increases or decreases rapidly, represented by a curve.

Front

How do you determine if a function is exponential?

Back

To determine if a function is exponential, check if it can be expressed in the form f(x) = a * b^x, where a is a constant and b is a positive number not equal to 1.

Front

What is the effect of a negative exponent in an exponential function?

Back

A negative exponent in an exponential function indicates a decay. For example, f(x) = 5 * (1/2)^x shows that as x increases, the function value decreases.