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(D) Let the initial population at the beginning of the first year be $x$.After the first year,the population increases by $5 \%$,so the population bec

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$10000$

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(D) Let the initial population at the beginning of the first year be $x$.After the first year,the population increases by $5 \%$,so the population becomes $x(1 + 0.05) = 1.05x$.After the second year,the population decreases by $5 \%$ from the population at the end of the first year,so the population becomes $1.05x(1 - 0.05) = 1.05x(0.95)$.Given that the final population is $9975$,we have the equation: $1.05x 	imes 0.95 = 9975$.$x 	imes (1.05 	imes 0.95) = 9975$.$x 	imes 0.9975 = 9975$.$x = \frac{9975}{0.9975} = 10000$.Therefore,the population at the beginning of the first year was $10000$.

During one year,the population of a town was increased by $5 \%$ and during the next year,the population decreased by $5 \%$. If the total population is $9975$ at the end of the second year,then what was the population size in the beginning of the first year?

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