⎩⎨⎧A(t)=P(1+nr)nt, whereA(t) is the account value at time tt is the number of yearsP is the initial investment, often called the principalr is the annual percentage rate (APR), or nominal raten is the number of compounding periods in one year
continuous growth formula
A(t)=aert, wheret is the number of unit time periods of growth
a is the starting amount (in the continuous compounding formula a is replaced with P, the principal)
e is the mathematical constant, e≈2.718282
Key Concepts
An exponential function is defined as a function with a positive constant other than 1 raised to a variable exponent.
A function is evaluated by solving at a specific value.
An exponential model can be found when the growth rate and initial value are known.
An exponential model can be found when the two data points from the model are known.
An exponential model can be found using two data points from the graph of the model.
An exponential model can be found using two data points from the graph and a calculator.
The value of an account at any time t can be calculated using the compound interest formula when the principal, annual interest rate, and compounding periods are known.
The initial investment of an account can be found using the compound interest formula when the value of the account, annual interest rate, compounding periods, and life span of the account are known.
The number e is a mathematical constant often used as the base of real world exponential growth and decay models. Its decimal approximation is e≈2.718282.
Scientific and graphing calculators have the key [ex] or [exp(x)] for calculating powers of e.
Continuous growth or decay models are exponential models that use e as the base. Continuous growth and decay models can be found when the initial value and growth or decay rate are known.
Glossary
annual percentage rate (APR)
the yearly interest rate earned by an investment account, also called nominal rate
compound interest
interest earned on the total balance, not just the principal
exponential growth
a model that grows by a rate proportional to the amount present
nominal rate
the yearly interest rate earned by an investment account, also called annual percentage rate
Licenses & Attributions
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Precalculus.Provided by: OpenStaxAuthored by: Jay Abramson, et al..Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions.License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175..