9.2 & 9.3 Exponential Growth and Decay CP

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. It can be represented by the function f(x) = a(b)^x, where b > 1.

Front

What is the formula for Exponential Decay?

Back

Exponential Decay is represented by the function f(x) = a(b)^x, where 0 < b < 1. It describes a situation where a quantity decreases by a consistent percentage over time.

Front

Identify the growth factor if the growth rate is 20%.

Back

The growth factor is 1.2.

Front

What does the 'a' value represent in the exponential function f(x) = a(b)^x?

Back

The 'a' value represents the initial amount or starting value at x = 0.

Front

If f(x) = 3(2)^x, what is the growth rate?

Back

The growth rate is 2 times.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.

Front

How do you calculate the growth factor from a percentage growth rate?

Back

To calculate the growth factor, convert the percentage to a decimal and add 1. For example, a growth rate of 30% gives a growth factor of 1.3.

Front

What is the formula to find the future value in exponential growth?

Back

The future value can be calculated using the formula: Future Value = Present Value * (1 + r)^t, where r is the growth rate and t is the time.

Front

If a population of bacteria doubles every hour, what type of growth is this?

Back

This is an example of Exponential Growth.

Front

What is the significance of the base 'b' in the exponential function?

Back

The base 'b' indicates the growth factor; if b > 1, it represents growth, and if 0 < b < 1, it represents decay.