Exponentials

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 range of any exponential function f(x) = a * b^x where a > 0?

Back

The range is (0, ∞). Exponential functions never reach zero.

Front

What is the value of any non-zero number raised to the power of 0?

Back

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, typically represented by f(x) = a * b^x where b > 1.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when the value decreases at a rate proportional to its current value, typically represented by f(x) = a * b^x where 0 < b < 1.

Front

Identify the type of function: f(x) = 4(0.89)^x. Is it growth or decay?

Back

Decay. Since the base (0.89) is less than 1.

Front

Identify the type of function: A = 1200(0.85)^6. Is it growth or decay?

Back

Decay. The base (0.85) is less than 1.

Front

What is the general form of an exponential growth function?

Back

f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

f(x) = a * b^x, where 0 < b < 1.

Front

If f(x) = 3(2)^x, what type of function is this?

Back

Exponential growth, because the base (2) is greater than 1.