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 y-intercept of the function f(x)=2(4)^x?

Back

The y-intercept (initial value) is 2.

Front

Classify the model A=10(1.01)^3 as Exponential GROWTH or DECAY.

Back

Growth.

Front

Classify the model A=1200(0.85)^6 as Exponential GROWTH or DECAY.

Back

Decay.

Front

What type of pattern do linear functions have?

Back

Linear functions add or subtract by the same number every time.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(1 + r)^x, where 'r' is the growth rate.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(1 - r)^x, where 'r' is the decay rate.

Front

How do you identify an exponential function from a table of values?

Back

If the ratio of consecutive outputs is constant, the function is exponential.

Front

What is the base of an exponential function?

Back

The base is the constant 'b' in the function f(x) = a(b)^x, which determines the rate of growth or decay.

Front

What does it mean if an exponential function has a base greater than 1?

Back

It indicates exponential growth.