Certainly! Let's solve the problem step by step to determine the number of deaths per year per thousand people for those who are 53 years old, given the formula:
[tex]\[ y = 0.034 x^2 - 2.8 x + 62.59 \][/tex]
Here, [tex]\( x \)[/tex] represents the age of the people, and we are given [tex]\( x = 53 \)[/tex].
1. Substitute [tex]\( x = 53 \)[/tex] into the formula:
[tex]\[ y = 0.034 (53)^2 - 2.8 (53) + 62.59 \][/tex]
2. Calculate [tex]\( 53^2 \)[/tex]:
[tex]\[ 53^2 = 2809 \][/tex]
3. Multiply [tex]\( 0.034 \)[/tex] by [tex]\( 2809 \)[/tex]:
[tex]\[ 0.034 \times 2809 = 95.506 \][/tex]
4. Multiply [tex]\( 2.8 \)[/tex] by [tex]\( 53 \)[/tex]:
[tex]\[ 2.8 \times 53 = 148.4 \][/tex]
5. Substitute these intermediate results back into the formula:
[tex]\[ y = 95.506 - 148.4 + 62.59 \][/tex]
6. Perform the arithmetic operations:
[tex]\[ y = 95.506 - 148.4 + 62.59 = 9.696 \][/tex]
Thus, the number of deaths per year per thousand people for 53-year-olds is approximately [tex]\( 9.696 \)[/tex].
7. Round the result to the nearest whole number:
[tex]\[ \boxed{10} \][/tex]
Therefore, approximately 10 people per thousand who are 53 years old die each year.
