section 3.1 vocabulary

Section 3.1 Vocabulary

Algebraic functions

•Include: Polynomial functions, and rational functions.

Exponential Function • The exponential function f

with base a is denoted by • f(x) = ax Where a > 0, a ≠ 1, and x is any

real number

The natural base•e ≈ 2.718281828…..

Natural Exponential Function

f(x) = ex

Continuous compounding Interest

• After t years, the balance A in an account with principal P and annual interest rate r is given by the following formula:

A = Pert

Interest (n) compoundings per year• After t years, the balance A in

an account with principal P and annual interest rate r is given by the following formula

A = P(1+ (r/n) ) nt

Section 3.2 Vocabulary

Logarithmic Function with base a

• For x > 0, a > 0, and a ≠ 1, y = log ax if and only if x = ay

The function given by f(x) = log ax

Is called the logarithmic function with base a

Common Logarithmic Function

• The logarithmic function with base 10 is called the common logarithmic function.

• Note: on most calculators this is denoted by the log button.

The Natural Logarithmic Function

• For x > 0y = ln (x) if and only if x = ey The function given by F(x) = loge(x) = ln(x)

Is called the natural logarithmic function.

Properties of Natural Logarithms

1.ln(1) = 0 because e0 = 1 2.ln(e) = 1 because e1 = e3.ln(ex) = x and e lnx = x4.If ln(x) = ln(y), then x = y

Section 3.3 Vocabulary

Change of Base Formula

•Log ax = log(x) / log(a)

•Log ax = ln(x) / ln(a)

Properties of Logs1. Product Property: loga(uv) = loga(u) + loga(v)

Quotient Property: 2. loga(u/v) = loga(u)- loga(v)

3. Power Property:loga(un) = nloga(u)

Section 3.4 Vocabulary

Section 3.5 Vocabulary

Mathematical Models

1. Exponential growth Model: Y = aebx , b > 02. Exponential Decay model: Y = ae-bx , b > 03. Gaussian model : Y = ae-(x-b)^2/c

4. Logistic growth modelY = 1/ (1 + be-rx)

5. Logistic models: Y = a + b ln(x)

Logistic Curve •S- shaped graph, given by the function:

Y = a /(1 + be-rx)