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 the base (a positive real number), and 'x' is the exponent.

Front

What does the base 'b' in an exponential function represent?

Back

The base 'b' represents the growth factor of the function. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a * b^x.

Front

How do you simplify the expression (2^3)(2^4)?

Back

(2^3)(2^4) = 2^(3+4) = 2^7.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where 'a' is the initial value and 'b' is the growth factor.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in value. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in value.

Front

How do you find the value of an exponential function at a specific point?

Back

To find the value of an exponential function at a specific point, substitute the value of 'x' into the function f(x) = a * b^x and calculate.

Front

What does the 'a' represent in the exponential function f(x) = a * b^x?

Back

The 'a' represents the initial value or the y-intercept of the function.

Front

How do you graph an exponential function?

Back

To graph an exponential function, plot the y-intercept (0, a), identify the growth or decay based on the base 'b', and draw a smooth curve that approaches the x-axis but never touches it.

Front

What is the simplified form of 10x^(-2)?

Back

10x^(-2) = 10 / (x^2).