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(b)^x, where b > 1.

Tags

CCSS.HSF-LE.A.1A

Front

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

Back

The growth factor is 2, meaning the quantity doubles with each unit increase in x.

Tags

CCSS.HSF-IF.C.8B

Front

How can you identify exponential growth from a function?

Back

You can identify exponential growth if the base of the exponent (b) is greater than 1 in the function f(x) = a(b)^x.

Tags

CCSS.HSF-IF.C.8B

Front

What does the term 'decay' mean in exponential functions?

Back

Decay refers to a decrease in quantity over time, represented by a function where the base of the exponent (b) is between 0 and 1.

Tags

CCSS.HSF-IF.C.8B

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

What does the equation A = 10(1.01)^3 represent?

Back

This equation represents exponential growth, as the base (1.01) is greater than 1.

Tags

CCSS.HSF-IF.C.8B

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

How do you determine the growth rate from an exponential function?

Back

The growth rate can be determined from the base of the exponent in the function f(x) = a(b)^x. If b = 2, the growth rate is 100% per unit increase in x.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

A smooth curve going up indicates exponential growth.

Tags

CCSS.HSF-IF.C.7E

Front

What is the significance of the coefficient in an exponential function?

Back

The coefficient (a) represents the initial value or starting amount before growth or decay begins.

Tags

CCSS.HSF-IF.C.8B