4.1 Exponential Basics

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 that accelerates as time goes on.

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 that slows down as time progresses.

Front

What is the general form of an exponential function?

Back

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

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified on a graph by a curve that rises steeply as it moves from left to right.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified on a graph by a curve that falls steeply as it moves from left to right.

Front

What does compounding mean in the context of exponential functions?

Back

Compounding refers to the process of earning interest on both the initial principal and the accumulated interest from previous periods.

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has already been added.

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 significance of the base in an exponential function?

Back

The base in an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What is an example of a real-world application of exponential functions?

Back

Real-world applications of exponential functions include population growth, radioactive decay, and compound interest in finance.