NCM1 Exponential Functions Review

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.

Front

What does the initial value in an exponential function represent?

Back

The initial value in an exponential function is the value of 'y' when 'x' is 0. It indicates the starting amount before any growth or decay occurs.

Front

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

Back

The initial value is 6.87.

Front

How do you represent a decay process in an exponential function?

Back

A decay process is represented by a base between 0 and 1 in the function y = a(b^x). For example, y = 5000(0.7)^x represents a decay of 30%.

Front

What is the equation for a culture of bacteria that starts with 5000 cells and dies by 30% each year?

Back

The equation is y = 5000(0.7)^x.

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 over time. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease over time.

Front

Identify the type of growth represented by the function f(x) = 0.25(1.3)^x.

Back

This function represents exponential growth.

Front

What is the equation for a flea medicine that breaks down at a rate of 20% per hour with an initial dose of 60 mg?

Back

The equation is y = 60(0.8)^x.

Front

What does the term 'rate of decay' mean in the context of exponential functions?

Back

The rate of decay refers to the percentage decrease in quantity over a specific time period, often represented as a base less than 1 in the exponential function.

Front

What is the general form of an exponential decay function?

Back

The general form is y = a(b^x), where 'a' is the initial amount and 'b' is a decay factor (0 < b < 1).