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Problem 31 Hard Difficulty

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?

Answer

(a) Using a computing device, we obtain a power function $N=c A^{b},$ where $c \approx 3.1046$ and $b \approx 0.308$.
(b) If $A=291,$ then $N=c A^{b} \approx 17.8,$ so you would expect to find 18 species of reptiles and amphibians on Dominica.

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Video Transcript

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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