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An amusement park opens and allows patrons to enter starting at 8:00 am at a rate of:

$$E(t)=3t^2+2t+3$$

After two hours, people start leaving at a rate of $L(t)=4t$.

The park policy allows families of small children and those who are handicapped or need assistance in at 7:45 am. So $21\text{ patrons}$ are in the park when it opens at 8:00 am.

How many patrons are in the park at 1:00 pm?

A

$136$

B

$147$

C

$168$

D

$204$

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