Math  /  Algebra

QuestionThe table shows projections for the female population of a country (in millions). \begin{tabular}{l|c|c|c} Year & 2020 & 2045 & 2050 \\ \hline Female Population & 181 & 227 & 236 \end{tabular} (a) Find a quadratic function f(x)=ax2+bx+c\mathrm{f}(\mathrm{x})=\mathrm{ax}{ }^{2}+\mathrm{bx}+\mathrm{c} that gives the female population (in millions) in year x , where x=0\mathrm{x}=0 corresponds to the year 2000 . (b) Estimate the female population in the year 2030 . (a) The coefficient of x2x^{2} in the equation is a=a= \square (Do not round until the final answer. Then round to three decimal places as needed.)

Studdy Solution
Simplify the expression:
f(30)=1750(900)+57.801+143    f(30)=1.2+57.801+143    f(30)=199.601 f(30) = -\frac{1}{750}(900) + 57.801 + 143 \implies f(30) = -1.2 + 57.801 + 143 \implies f(30) = 199.601
Solution: (a) The coefficient of x2x^2 in the equation is a=17500.001a = -\frac{1}{750} \approx -0.001 (to three decimal places). (b) The estimated female population in the year 2030 is approximately 199.601199.601 million.

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