Exponential Growth & Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay describes a decrease in quantity where the rate of decrease is proportional to the current amount, resulting in a rapid decline that slows over time.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

The variable 'a' represents the initial amount or starting value in the exponential function.

Tags

CCSS.HSF.LE.B.5

Front

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

Back

The variable 'b' is the base of the exponential function, representing the growth (b > 1) or decay (0 < b < 1) factor.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify exponential growth from a function?

Back

Exponential growth can be identified if the base 'b' in the function f(x) = a(b)^x is greater than 1.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify exponential decay from a function?

Back

Exponential decay can be identified if the base 'b' in the function f(x) = a(b)^x is between 0 and 1.

Tags

CCSS.HSF-IF.C.8B

Front

What is the common ratio in the function f(x) = 300(1.16)^x?

Back

The common ratio is 1.16, indicating a 16% increase for each unit increase in x.

Front

If a function is modeled as A = 1200(0.85)^6, what type of model is it?

Back

This model represents exponential decay because the base 0.85 is less than 1.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for calculating the future value in exponential growth?

Back

The formula is A = P(1 + r)^t, where A is the future value, P is the principal amount, r is the rate of growth, and t is the time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for calculating the future value in exponential decay?

Back

The formula is A = P(1 - r)^t, where A is the future value, P is the principal amount, r is the rate of decay, and t is the time.

Tags

CCSS.HSF-IF.C.8B