Algebra 1: 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 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 does the base 'b' represent in an exponential function?

Back

The base 'b' in an exponential function represents 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' is greater than 1 in the function f(x) = a(b^x).

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' is between 0 and 1 in the function f(x) = a(b^x).

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth equation?

Back

The general form of an exponential growth equation is y = a(1 + r)^x, where 'r' is the growth rate.

Front

What is the general form of an exponential decay equation?

Back

The general form of an exponential decay equation is y = a(1 - r)^x, where 'r' is the decay rate.

Tags

CCSS.HSF-IF.C.8B

Front

If a population of bacteria doubles every hour, what type of function models this situation?

Back

This situation is modeled by an exponential growth function.

Front

Write the exponential decay function for a quantity that decreases by 20% each year starting from 100 units.

Back

y = 100(0.8)^x.

Tags

CCSS.HSF.LE.A.2

Front

What is the formula to calculate the amount after 't' years for an initial amount 'P' with a growth rate 'r'?

Back

The formula is A = P(1 + r)^t.

Tags

CCSS.HSF-IF.C.8B