Exponential Functions Flashcard Review

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 a positive real number, and x is the exponent. It represents growth or decay processes.

Front

What does it mean to vertically shrink a graph by a factor of \( \frac{1}{2} \)?

Back

A vertical shrink by a factor of \( \frac{1}{2} \) means that every y-value of the function is multiplied by \( \frac{1}{2} \), making the graph closer to the x-axis.

Front

How do you shift a graph to the right by 3 units?

Back

To shift a graph to the right by 3 units, replace x with (x - 3) in the function's equation.

Front

What does it mean to move a graph down by 5 units?

Back

Moving a graph down by 5 units means subtracting 5 from the entire function, resulting in f(x) - 5.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 0 < b < 1.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the half-life of a substance?

Back

The half-life of a substance is the time required for half of the substance to decay or be eliminated.

Front

How do you calculate the remaining amount of a substance after a certain time using half-life?

Back

To calculate the remaining amount, use the formula: Remaining Amount = Initial Amount * (1/2)^(t/half-life), where t is the total time elapsed.

Front

What is the percentage rate of change in an exponential function?

Back

The percentage rate of change in an exponential function is given by (b - 1) * 100%, where b is the base of the exponential function.