Exponential Functions and Log

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 does the base of an exponential function represent?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth function?

Back

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

Front

What is the general form of an exponential decay function?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate the half-life of a substance?

Back

The half-life can be calculated using the formula t(1/2) = ln(2) / k, where 'k' is the decay constant.

Front

What does the term 'logarithm' mean?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number.

Tags

CCSS.HSF.BF.B.5

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive base k.

Front

What is the value of log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.

Tags

CCSS.HSF.BF.B.5

Front

What does the term 'common ratio' refer to in exponential functions?

Back

The common ratio is the factor by which a quantity increases or decreases in each time period in a geometric sequence.

Front

How do you determine the number of intervals in a decay problem?

Back

To determine the number of intervals, divide the total time by the time per interval.

Tags

CCSS.HSF-LE.A.1C