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P(x)=2,500(0.98)^(x)
The function models 
P, the population of the village of Kalm 
x years after 1997. Based on the model, what is the population of Kalm 18 years after 1997 ?
Choose 1 answer:
(A) 2,450
(B) 2,127
(C) 1,846
(D) 1,738

P(x)=2,500(0.98)x P(x)=2,500(0.98)^{x} \newlineThe function models P P , the population of the village of Kalm x x years after 19971997. Based on the model, what is the population of Kalm 1818 years after 19971997 ?\newlineChoose 11 answer:\newline(A) 22,450450\newline(B) 22,127127\newline(C) 11,846846\newline(D) 11,738738

Full solution

Q. P(x)=2,500(0.98)x P(x)=2,500(0.98)^{x} \newlineThe function models P P , the population of the village of Kalm x x years after 19971997. Based on the model, what is the population of Kalm 1818 years after 19971997 ?\newlineChoose 11 answer:\newline(A) 22,450450\newline(B) 22,127127\newline(C) 11,846846\newline(D) 11,738738
  1. Identify Function and Value: Identify the given function and the value to substitute for xx.\newlineThe function given is P(x)=2,500(0.98)xP(x) = 2,500(0.98)^x, which models the population of the village of Kalm xx years after 19971997. We need to find the population 1818 years after 19971997, so we will substitute xx with 1818.
  2. Substitute xx with 1818: Substitute xx with 1818 in the function to calculate the population.P(18)=2,500(0.98)18P(18) = 2,500(0.98)^{18}
  3. Calculate (0.98)18(0.98)^{18}: Calculate the value of (0.98)18(0.98)^{18}. Using a calculator, we find that (0.98)180.689478(0.98)^{18} \approx 0.689478.
  4. Multiply by 22,500500: Multiply the result from Step 33 by 2,5002,500 to find the population.\newlineP(18)=2,500×0.6894781,723.695P(18) = 2,500 \times 0.689478 \approx 1,723.695
  5. Round to Nearest Whole Number: Round the result to the nearest whole number, as population is typically expressed as a whole number.\newlineP(18)1,724P(18) \approx 1,724

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