Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth function?

Back

The general form is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is the general form of an exponential decay function?

Back

The general form is f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

If a population of bears decreases by 2% each year, what is the decay rate in decimal form?

Back

The decay rate in decimal form is 0.02.

Tags

CCSS.HSF-LE.A.1C

Front

How do you represent a population that decreases by a percentage each year?

Back

You represent it using the function B = a(1 - r)^t, where 'a' is the initial population, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF.BF.A.2

Front

What does the base of an exponential function represent?

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The base of an exponential function represents the growth factor (if greater than 1) or decay factor (if between 0 and 1) of the function.

Tags

CCSS.HSF-IF.C.8B

Front

What is the value of a home worth today if it was purchased for $160,000 and appreciates at 5% per year for 20 years?

Back

The home is worth approximately $424,527.63 today.

Tags

CCSS.HSF.BF.A.2

Front

What does it mean if an exponential function has a base greater than 1?

Back

If the base is greater than 1, the function represents exponential growth.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean if an exponential function has a base between 0 and 1?

Back

If the base is between 0 and 1, the function represents exponential decay.

Tags

CCSS.HSF-IF.C.8B