City planners anticipate an 8.2% population growth per year, including new residents and births. The population, in millions of people, based on this increase can be modeled by the function p(x) = 2.5(1.082)x, where x is the number of years of tracked growth. The planners also estimate a 3% population loss over the same time period that can be modeled by the function L(p) = p(0.97)x.
Substitute p(x) = 2.5(1.082)^x into the loss model: L(p(x)) = 2.5(1.082)^x(0.97)^x. Since the exponents are both x, multiply the growth and loss factors: 1.082 × 0.97 = 1.04954. Thus L(p(x)) = 2.5(1.04954)^x, which is choice D.
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