Ecology—Mediterranean Fish Catches: The annual amount of fish caught by Slovenians from 2000 to 2010 in the Mediterranean Sea can be modeled by
f(x) = 19.46e−0.13x 0 ≤ x ≤ 10
where x represents the number of years since 2000 and f(x) represents the amount of fish caught in tons. (Source: EuroStat.)
(a) Classify the model as an exponential growth or exponential decay model.
(b) Evaluate f(2) and interpret.
(c) Compute the slope of the secant line for x = 2 and Δx = 6. Comparing this result to Exercise 1, which country has the greatest decrease in fish catches, Norway or Slovenia?
Exercise 1
Ecology—Atlantic Fish Catches: During the 1950s and 1960s, the global expansion of fisheries was coupled with ever-growing catches at a rate so rapid that they tended to exceed fish population growth. (Source: Institute of Development Research.) The annual amount of fish caught by Norwegians from 2000 to 2010 in the northwest Atlantic Ocean can be modeled by
f(x) = 30,111e−0.22x 0 ≤ x ≤ 10
where x represents the number of years since 2000 and f(x) represents the amount of fish caught in tons. (Source: EuroStat.)
Compute the slope of the secant line for x = 2 and Δx = 6. Does this result support the Institute’s claim?
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