Exponential Functions

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 a positive real number, and x is the exponent.

Front

What is the general form of an exponential equation?

Back

The general form of an exponential equation is y = a * b^x, where a is the initial value and b is the base of the exponential.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

How do you identify the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is found by evaluating the function at x = 0, which gives y = a.

Front

What is the y-intercept of the function y = 3 * 2^x?

Back

The y-intercept is 3, as it is the value of the function when x = 0.

Front

How do you simplify the expression (3x^4)(5x^3)?

Back

To simplify, multiply the coefficients (3 * 5 = 15) and add the exponents of x (4 + 3 = 7), resulting in 15x^7.

Front

What is the product rule for exponents?

Back

The product rule states that when multiplying two exponential expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).

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.

Front

What does it mean for a function to be exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a * b^x, where the variable x is in the exponent.

Front

How do you determine if a graph represents an exponential function?

Back

A graph represents an exponential function if it shows a rapid increase or decrease, forming a curve that is not a straight line.