Let the growth function be the polynomial
f(x) = ax³ + bx² + cx + d
From the given information,
f(1)=1, therefore
a + b + c + d = 1 (1)
f(2) = 9, therefore
8a + 4b + 2c + d = 9 (2)
f(3) = 20, therefore
27a + 9b + 3c + d = 20 (3)
f(4) = 34, therefore
64a + 16b + 4c + d = 34 (4)
Assemble the four equations into the matrix equation (also shown in the figure)
| 1 1 1 1 | 1 |
| 8 4 2 1 | 9 |
|27 9 3 1 | 20 |
|64 16 4 1 | 34 |
Solve with the graphing calculator to obtain
a = 0
b = 1.5
c = 3.5
d = -4
Therefore
f(x) = 1.5x² + 3.5x - 4
After 7 days,
f(7) = 1.5*49 + 3.5*7 - 4 = 94
Answer: D. 94
