Mr. Souza posted a pic of the math team on Instagram, and it has gone viral. Every day, he checks how many new comments it got. On the day he posted it (𝑡=0), the post got 10 comments. Two days later (𝑡=2), the post got 51 new comments. Five days after posting (𝑡=5), the post got 45 new comments.
Mr. Souza has reason to believe the number of new comments 𝑡 days after posting may be modeled well by 𝐶𝑡=𝑎𝑡2+𝑏𝑡+𝑐.
A) Use the given data to write three equations that can be used to find the values for constants 𝑎, 𝑏, and 𝑐 in the expression for 𝐶𝑡.
B) Find the values for 𝑎, 𝑏, and 𝑐 as decimal approximations.