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The table shows the number $ N $ of species of reptiles and amphibians inhabiting Caribbean islands and the area $ A $ of the island in square miles.

(a) Use a power function to model N as a function of $ A $.(b) The Caribbean island of Dominica has area $ 291 mi^2 $. How many species of reptiles and amphibians would you expect to find on Dominica?

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01:06

Clarissa Noh

02:09

Heather Zimmers

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 2

Mathematical Models: A Catalog of Essential Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Missouri State University

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

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A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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So here we're using um calculating device in order to moderately given data. So we have um a model showing the species of reptiles, the number of them um amphibians inhabiting the caribbean islands, depending on the area. So we end up getting we know the number is going to be equal to see times A. To the B. And we see that he is going to be about 3.1 046 and then A. Is going to be about 2 91. And our value um it's getting a resulting in 0.3 08 So this is our function of a. This is okay. B is going to use 0.308 And we see that the A value if A is 2 91 we end up getting about 18. Is the number of reptiles. Yeah.

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