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Using data and projections from 1990 through 2050, the percent of Group $\mathrm{H}$ in a country's population is given by $H(x)=0.224 x+9.4$, where $x$ is the number of years after 1990 . Find the years when the population of Group $H$ is projected to be at least $15 \%$ of the country's population.
Choose the correct response below and, if necessary, fill in the answer box to complete your choice
A. Between the year and the year $\square$ (Type a whole number)
B. The year and before (Type a whole number.)
C. The year and after (Type a whole number)
D. The population of Group $\mathrm{H}$ will never exceed $15 \%$

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Answer

Final Answer: The population of Group H is projected to be at least 15% of the country's population in the year \(\boxed{2015}\) and after. Therefore, the correct response is C. The year 2015 and after.

Steps

Step 1 :We need to find the year when the population of Group H is projected to be at least 15% of the country's population. This means we need to solve the equation \(H(x) = 15\) for \(x\). Since \(H(x) = 0.224x + 9.4\), we can set up the equation \(0.224x + 9.4 = 15\) and solve for \(x\). The value of \(x\) will give us the number of years after 1990 when the population of Group H is projected to be at least 15%.

Step 2 :The solution to the equation is 25. This means that 25 years after 1990, the population of Group H is projected to be at least 15% of the country's population. However, the question asks for the year, not the number of years after 1990. Therefore, we need to add 1990 to our solution to get the year.

Step 3 :Final Answer: The population of Group H is projected to be at least 15% of the country's population in the year \(\boxed{2015}\) and after. Therefore, the correct response is C. The year 2015 and after.

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