Biologists have long noticed a relationship between the area of a piece of land and the number of species found there. The following data shows a sample of the British Isles and how many vascular plants are found on each.

(a) One common model for this relationship is logarithmic. Using the logarithmic regression feature on a graphing calculator, find a logarithmic function that best fits the data.
(b) An alternative to the logarithmic model is a power function of the form S = b(A^c). Using the power regression feature on a graphing calculator, find a power function that best fits the data.
(c) Graph both functions from parts (a) and (b) along with the data. Give advantages and drawbacks of both models.
(d) Use both functions to predict the number of species found on the isle of Shetland, with an area of 984.2 km². Compare with the actual number of 421.

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Isle Ailsa Fair Iona Man N. Ronaldsay Skye Stronsay Wight Area (km²) 0.8 5.2 9.1 571.6 7.3 1735.3 35.2 380.7 Species 75 174 388 765 131 594 62 1008