Personal Finance—Bank Credit Cards: A topic that has gained attention since the mid-2000s...

Personal Finance—Bank Credit Cards: A topic that has gained attention since the mid-2000s is the growing private credit card debt in the United States. The number of bank-issued credit cards in circulation annually in the United States can be modeled by

 f(x) = − 10.8x2 + 82.8x + 455 0 ≤ x ≤ 10

where x represents the number of years since 2000 and f(x) represents the number of bank-issued credit cards in circulation annually, measured in millions. (Source: The Nilson Report.)

(a) Evaluate dy for x = 8 and Δx = dx = 1 and interpret.

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(b) Write the equation of the tangent line of f at x = 8 and evaluate the equation for the year 2012. Interpret this result.