Modeling 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

Identify the initial value in the function y = 6.87(4)^x.

Back

The initial value is 6.87.

Front

Which of the following is an exponential function? y = x^2, f(x) = 3x^3, y = x^3, f(x) = 3^x.

Back

f(x) = 3^x is an exponential function.

Front

What is the value of b^0?

Back

b^0 = 1 for any non-zero b.

Front

What is the initial value in the function y = 4(2)^x?

Back

The initial value is 4.

Front

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

Back

The y-intercept is 3.

Front

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

Back

The base 'b' represents the growth factor in an exponential function.

Front

If a function has a base greater than 1, what type of growth does it exhibit?

Back

It exhibits exponential growth.

Front

If a function has a base between 0 and 1, what type of decay does it exhibit?

Back

It exhibits exponential decay.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where 'a' is the initial value and 'b' is the base.