Exponential Growth and Decay Day 1

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(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. It can be represented by the function f(x) = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth or decay factor. For example, in f(x) = a(b)^x, if b > 1, it represents growth; if 0 < b < 1, it represents decay.

Front

In the function f(x) = 3(2)^x, how many ants were there initially?

Back

There were 3 ants initially, as indicated by the coefficient '3' in the function.

Front

What does a smooth curve going up indicate in a graph?

Back

A smooth curve going up indicates exponential growth.

Front

What does a smooth curve going down indicate in a graph?

Back

A smooth curve going down indicates exponential decay.

Front

In the function A = 1200(0.85)^6, what type of model is this?

Back

This model is an example of exponential decay.

Front

What is the growth rate in the function f(x) = 3(2)^x?

Back

The growth rate is 2 times, meaning the number of ants doubles with each unit increase in x.

Front

How can you identify exponential growth from a graph?

Back

Exponential growth can be identified by a curve that rises steeply as x increases.

Front

How can you identify exponential decay from a graph?

Back

Exponential decay can be identified by a curve that falls steeply as x increases.