Agriculture—Peruvian Imports: For the model in Exercise 1, write the equation of the line tangent to the graph of f at the point (21, f(21)), then evaluate the tangent line equation when x = 30. Interpret the meaning of this ordered pair.
Exercise 1
Agriculture—Peruvian Imports: The American appetite for fresh produce has resulted in a rise in agricultural imports from Latin American countries. One country that has benefited from this is Peru, which supplements California’s supply of avocados. “California doesn’t affect us, as demand and consumption in the U.S. are very high,” said Arturo Medina, general manager of the Association of Prohass. (Source: Fresh Plaza.) The amount of agricultural exports from Peru to the United States from 1990 to 2011 can be modeled by the exponential function
f(x) = 56.53e0.14x 0 ≤ x ≤ 21
where x represents the number of years since 1990, and f(x) represents the annual amount of agricultural exports from Peru to the United States, measured in millions of dollars. (Source: U.S. Department of Agriculture.)
(a) Determine f′(x).
(b) Evaluate f′(21) and interpret.
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