A newly opened juice shop earned a profit of $2,400 in the first month. For the remaining months of the year, the expected profit is modeled by the function J (t) = 2.5t + 1,250, where t is the number of months after the first month the shop opened. Create a function, P (t), that describes the total profit earned for the entire year.

First month's profit of the company = $2,400.

After the first month, the profit is modeled by the function

J (t) = 2.5t + 1,250, t is the number of months after the first month the shop opened.

Now, P (t) describes the total profit earned by the company.

So, P (t) = (Profit earned from first month) + (Profit earned from remaining 11 months of the year)

= 2400 + (2.5t + 1250)

= 2.5t + 3650

Hence, total profit earned for the year = 2.5t + 3650.