A farm in Canada has 228 alpacas. After 8 years, the alpaca population decreased to 186 alpacas. The function f (t) = 228 (0.975) ^t models the population of alpacas in the Canadian farm as a function of time in years. How many alpacas will there be in 20 years?

Question

Rosemary Conley

Mathematics

16 December, 16:10

A farm in Canada has 228 alpacas. After 8 years, the alpaca population decreased to 186 alpacas. The function f (t) = 228 (0.975) ^t models the population of alpacas in the Canadian farm as a function of time in years. How many alpacas will there be in 20 years?

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Alessandra Blackburn · Answer 1

After 20 years there will be 137 alpacas on the farm. Since the function has a value less than 1.0 raised to a power, in this case 20, that value will always be less than 1.0. Therefore we can presume that the final value will be less than 228, which the information states a decreasing population.