Unit 6: Exponential and Logarithmic Functions

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.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease.

Tags

CCSS.HSF-IF.C.8B

Front

Identify the general form of an exponential function.

Back

The general form is f(x) = a * b^x, where a is the initial value, b is the growth (b > 1) or decay (0 < b < 1) factor.

Tags

CCSS.HSF.LE.A.2

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number. For example, in log_b(a) = c, b is the base.

Tags

CCSS.HSF.BF.B.5

Front

How do you convert from exponential form to logarithmic form?

Back

To convert from exponential form a^b = c to logarithmic form, use log_a(c) = b.

Tags

CCSS.HSF.BF.B.5

Front

Solve for x: 2^(x+1) = 16.

Back

x = 3.

Tags

CCSS.HSF.LE.A.4

Front

What is the logarithmic identity for log_a(a) ?

Back

log_a(a) = 1, because a raised to the power of 1 equals a.

Front

What is the logarithmic identity for log_a(1) ?

Back

log_a(1) = 0, because a raised to the power of 0 equals 1.

Front

Rewrite the logarithmic equation log_5(25) = 2 in exponential form.

Back

5^2 = 25.

Tags

CCSS.HSF.BF.B.5

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other.

Tags

CCSS.HSF.BF.B.5