Download - Section 3.1 Vocabulary
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Section 3.1 Vocabulary
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Algebraic functions
•Include: Polynomial functions, and rational functions.
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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
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The natural base•e ≈ 2.718281828…..
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Natural Exponential Function
f(x) = ex
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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
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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
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Section 3.2 Vocabulary
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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
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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.
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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.
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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
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Section 3.3 Vocabulary
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Change of Base Formula
•Log ax = log(x) / log(a)
•Log ax = ln(x) / ln(a)
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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)
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Section 3.4 Vocabulary
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Section 3.5 Vocabulary
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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)
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Logistic Curve •S- shaped graph, given by the function:
Y = a /(1 + be-rx)