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 Dependent Variable

 Number of inequalities to solve: 23456789
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 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg: Section 3.4 Modeling continuous relationship which is
increasing and concave down

Model: Cost Function A company manufactures a
quantity q of a product per month.
They invest \$2.3 million in capital
towards technology (machinery,
computers, etc.) and a fixed cost
investment of \$5.4 million. Data
is collected on the cost for varying
quantities q (in 100,000 units). Determine a model for cost. Cost Data Properties of Model Is the data increasing or decreasing? Cost increases as production increases Is the data concave up or concave down? Data is concave down Use the Ladder of Powers to determine a
model with these characteristics. Can it be a
polynomial model? No, polynomial functions are either increasing
concave up or decreasing concave down Function of form where p(x) is a polynomial, integer n>1 If n is even, what is the domain of r(x)? If n is odd, what is the domain of r(x)? What is the concavity of a radical power
function y = axn when 0 < n < 1?

index 0<n<1  Ladder of Powers to decide if n = ½,
n = 1/3, n = ¼ etc. Graph and , which is
a better fit to the Cost Data? Use Derive or a graphing calculator to fit a Solution:  Cobb-Douglas Production Function

Cost Model -Algebraic Method Isolate the radical expression Undo the nth root by using the inverse
function –the nth power For which nth roots do we need to check for
extraneous roots? If nth root is even, taking an even power can
result in extraneous roots If nth root is odd, taking an odd power will not
result in extraneous roots Isolate one of the radical expressions Take the square to remove one of the square roots Isolate the remaining radical and square again Check for extraneous roots Solve using algebraic and graphic method  Class Participation Exercise

1. Determine what
type of function
has the given
graph? Is it
polynomial or

2. Solve the following radical equation:  Linearization Use radical function to
make nonlinear polynomial
data linear Model the linear data Convert linear model into
polynomial model Linearization Use Derive or graphing calculator to
plot data and transformed data  Which of these makes the data linear?

Linearization –Transformed Data  Linearization –Data Plot Linearization Which transformed data is linear? Solution: Cube root, so data is modeled by
a cubic function Linearized data model: y = 1.3x + 0.77 Actual data model:  Best fit cubic model: 