Answer
The quadratic model for this data
n = -2t² + 24t + 10
Step-by-step explanation
Quadratic functions are given as
y = ax² + bx + c
where y = n, t = x and a, b and c are constants.
n = at² + bt + c
when t = 1, n = 32
32 = a(1)² + b(1) + c
32 = a + b + c
when t = 3, n = 64
64 = a(3)² + b(3) + c
64 = 9a + 3b + c
when t = 4, n = 74
74 = a(4)² + b(4) + c
74 = 16a + 4b + c
Combining the three equations
a + b + c = 32
9a + 3b + c = 64
16a + 4b + c = 74
We can then solve this simultaneously and obtain that
a = -2
b = 24
z = 10
So, the quadratic model for this data
n = -2t² + 24t + 10
Hope this Helps!!!