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.
Find the average rate of change of the number of new comments over the interval 2≤𝑡≤5.
Use that average rate of change to predict the number of new comments the post got on day 𝑡=4.
Is this an overapproximation or underapproximation of the value of 𝐶4?