Exponential Functions Warm Up

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 decay factor represent in exponential decay?

Back

The decay factor represents the fraction of the quantity that remains after each time period. For a decay rate of 20%, the decay factor is 0.8.

Front

If the decay rate is 20%, what is the decay factor?

Back

0.8

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

Front

How can you identify exponential decay in a function?

Back

Exponential decay can be identified by a base 'b' that is between 0 and 1 in the function f(x) = a * b^x.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a * b^x, where 0 < b < 1.

Front

What does the term 'exponential growth' mean?

Back

Exponential growth refers to an increase in a quantity where the growth rate is proportional to the current value, leading to faster increases over time.

Front

Classify the model A=1200(0.85)^6 as growth or decay.

Back

Decay.

Front

What is an example of exponential growth?

Back

An example of exponential growth is population growth, where the population increases by a fixed percentage each year.

Front

What is the decay rate if the decay factor is 0.5?

Back

The decay rate is 50%.