The number of species of a given taxonomic group within a given habitat (often an island) is a function of the area of the habitat. For islands in the West Indies, the formula below approximates the number S of species of amphibians and reptiles on an island in terms of the island area A in square miles.S(A) = 3 A0.3This is an example of a species-area relation.(a) Make a table giving the value of S for islands ranging in area from 4,000 to 28,000 square miles. (Round your answers to two decimal places.)A(square miles)S(A)4,000 8,000 12,000 16,000 20,000 24,000 28,000 (b) Explain in practical terms what S(24,000) means. Calculate that value. (Round your answer to two decimal places.)S(24,000) =   (c) Use functional notation to express the number of species on an island whose area is 8,200 square miles.S(   )Calculate that value. (Round your answer to two decimal places.)  (d) Would you expect a graph of S to be concave up or concave down?

Question
Asked Sep 27, 2019

The number of species of a given taxonomic group within a given habitat (often an island) is a function of the area of the habitat. For islands in the West Indies, the formula below approximates the number S of species of amphibians and reptiles on an island in terms of the island area A in square miles.

S(A) = 3 A0.3

This is an example of a species-area relation.

(a) Make a table giving the value of S for islands ranging in area from 4,000 to 28,000 square miles. (Round your answers to two decimal places.)
A
(square miles)
S(A)
4,000  
8,000  
12,000  
16,000  
20,000  
24,000  
28,000  

(b) Explain in practical terms what S(24,000) means. 

Calculate that value. (Round your answer to two decimal places.)
S(24,000) =   

(c) Use functional notation to express the number of species on an island whose area is 8,200 square miles.
S(   )

Calculate that value. (Round your answer to two decimal places.)
  
(d) Would you expect a graph of S to be concave up or concave down?
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Expert Answer

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Step 1

a) Make the table giving the value of S for ranging i...

S(A) 3.403
S(4000) 3(4000)
A
0.3
4000
36.12
8000
0.3
S(8000) 3(8000)
44.47
22
12000
0.3
S(12000)-3(12000)
50.22
16000
0.3
S(16000) 3(16000)
54.75
0.3
20000
S(20000) 3(20000)
58.54
24000
0.3
S(24000) 3(24000)
61.83
28000
0.3
S(28000) 3(28000)3
64.75
22
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S(A) 3.403 S(4000) 3(4000) A 0.3 4000 36.12 8000 0.3 S(8000) 3(8000) 44.47 22 12000 0.3 S(12000)-3(12000) 50.22 16000 0.3 S(16000) 3(16000) 54.75 0.3 20000 S(20000) 3(20000) 58.54 24000 0.3 S(24000) 3(24000) 61.83 28000 0.3 S(28000) 3(28000)3 64.75 22

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