To solve the problem of finding the number of flu virus particles in a person's body 2 days after being infected, we need to substitute [tex]\( x = 2 \)[/tex] into the given polynomial equation and evaluate it.
The polynomial given is:
[tex]\[ y = -0.78 x^4 + 3.2 x^3 + 26.5 \][/tex]
Step-by-Step Solution:
1. Substitute [tex]\( x = 2 \)[/tex] into the polynomial:
[tex]\[ y = -0.78 (2)^4 + 3.2 (2)^3 + 26.5 \][/tex]
2. Calculate each term separately:
- Evaluate [tex]\( (2)^4 \)[/tex]:
[tex]\[ (2)^4 = 16 \][/tex]
- Multiply by the coefficient for the first term:
[tex]\[ -0.78 \times 16 = -12.48 \][/tex]
- Evaluate [tex]\( (2)^3 \)[/tex]:
[tex]\[ (2)^3 = 8 \][/tex]
- Multiply by the coefficient for the second term:
[tex]\[ 3.2 \times 8 = 25.6 \][/tex]
3. Combine all the terms to get [tex]\( y \)[/tex]:
[tex]\[ y = -12.48 + 25.6 + 26.5 \][/tex]
4. Add these values together:
[tex]\[ y = 39.62 \][/tex]
Thus, there are [tex]\( 39.62 \)[/tex] billion flu virus particles in a person's body 2 days after being infected.
So, the final answer in the blank is:
[tex]\[ \boxed{39.62} \][/tex]
There are [tex]\( 39.62 \)[/tex] billion virus particles in a person's body 2 days after being infected.
