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, represented by the function f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

Front

What is exponential decay?

Back

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

Front

How can you identify exponential decay in a function?

Back

You can identify exponential decay if the base of the exponent is less than one, such as in the function f(x) = 90(1/2)^x.

Front

How can you identify exponential growth in a function?

Back

You can identify exponential growth if the base of the exponent is greater than one, such as in the function f(x) = 3(2)^x.

Front

What does the initial value in an exponential function represent?

Back

The initial value in an exponential function represents the starting amount before any growth or decay occurs.

Front

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

Back

There were 3 ants initially.

Front

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

Back

Decay.

Front

Classify the model A=10(1.01)^3 as growth or decay.

Back

Growth.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(1 + r)^x.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(1 - r)^x.