Exponential Functions

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Presentation transcript:

Exponential Functions Chapter 1 Prerequisites for Calculus Section 1.3 Exponential Functions

Bellwork

Quick Review Solutions

What you’ll learn about Exponential functions Rules of exponents Applications of exponential functions (growth and decay) Compound interest The number e …and why Exponential functions model many growth patterns.

Exponential Function

Exponential Growth

Exponential Growth

Rules for Exponents

Half-life Exponential functions can also model phenomena that produce decrease over time, such as happens with radioactive decay. The half-life of a radioactive substance is the amount of time it takes for half of the substance to change from its original radioactive state to a non-radioactive state by emitting energy in the form of radiation.

Exponential Growth and Exponential Decay

Example Finding Zeros

Compound Interest Formula If an account begins with principal P and earns an annual interest rate r compounded n times per year, then the value of the account in t years is

The Number e

The Number e

Example The Number e

Example The Number e

Continuously Compounded Interest Formula If an account begins with principal P and earns an annual interest rate r compounded continuously, then the value of the account in t years is

Homework Section 1.3: 2,4,10, 12, 14, 16, 40, 44

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3

Quick Quiz Sections 1.1 – 1.3