The number of people , d, in thousands applying for medical benefits per week in a particular city can be modules by the equation d(t)=2.5 sin(0.76t+0.3)+3.8 where t is the time in years since January 2000. Based on the equation The Maximum number of people in thousands apply for benefits per year in the city is

Step-by-step explanation:

Given the number of people d, in thousands applying for medical benefits per week in a particular city c modeled by the equation d(t)=2.5 sin(0.76t+0.3)+3.8 where t is the time in years, the maximum number of people tat will apply will occur at d(t)/dt = 0

Differentiating the function given with respect to t, we will have;

First we need to know that differential of any constant is zero.

If then;

To know the maximum number of people in thousands that apply for benefits per year in the city, we wil substitute the value of t = 29.75 into the modeled equation

Since d is in thousands, the maximum number of people in thousands will be 4.7732*1000 = 4773.2 which is approximately 4773 peoples.

the solution is 12x-6y