Final answer:
To write a cubic model for the number of graduates in a given year since 2002, choose three points from the table and solve the equations to find the coefficients of the cubic function.
Step-by-step explanation:
To write a cubic model for the number of graduates in a given year since 2002, we need to find three points on the graph and then use them to write the equation of a cubic function.
Let's assume that the years since 2002 are represented by the variable x and the number of graduates is represented by the variable y. From the given table, we can choose three points such as (0, 10000), (4, 20000), and (6, 30000).
Using these three points, we can set up three equations:
10000 = a(0)^3 + b(0)^2 + c(0) + d
20000 = a(4)^3 + b(4)^2 + c(4) + d
30000 = a(6)^3 + b(6)^2 + c(6) + d
Simplifying these equations, we get:
d = 10000
64a + 16b + 4c + d = 20000
216a + 36b + 6c + d = 30000
Solving these equations will give us the values of a, b, and c. Once we have these values, we can substitute them into the general cubic form equation y = ax^3 + bx^2 + cx + d to get the cubic model for the number of graduates in a given year since 2002.
To estimate the number of graduates in 2008, we can substitute x = 6 into the cubic model equation and solve for y.
Hope this helps!