To determine how many corn plants will be infected with Common Corn Rust after 10 days, we will use the given exponential model \( y = 8000 \left( 1 - e^{-0.03 t} \right) \). Here, \( y \) represents the number of infected plants, and \( t \) represents the number of days since the first case of the disease.
We are tasked with finding the number of infected plants after 10 days, so we will substitute \( t = 10 \) into the model.
1. Substitute \( t = 10 \) into the equation:
[tex]\[ y = 8000 \left( 1 - e^{-0.03 \times 10} \right) \][/tex]
2. Simplify the exponent in the exponential term:
[tex]\[ y = 8000 \left( 1 - e^{-0.3} \right) \][/tex]
3. Compute \( e^{-0.3} \) using the exponential constant \( e \):
[tex]\[ e^{-0.3} \approx 0.7408182207 \][/tex]
4. Substitute the value back into the equation:
[tex]\[ y = 8000 \left( 1 - 0.7408182207 \right) \][/tex]
5. Subtract \( 0.7408182207 \) from 1:
[tex]\[ y = 8000 \left( 0.2591817793 \right) \][/tex]
6. Multiply the constants:
[tex]\[ y \approx 2073.454234546257 \][/tex]
After completing the calculations, we find that approximately 2073 plants will be infected with Common Corn Rust after 10 days. Thus, the correct answer is 2073.
