Arare bacterial culture is being grown in a lab. as time passes, the cells multiply in a specific pattern. after 1 day, there is only 1 cell. after 2 days, there are 9 cells. after 3 days, there are 20 cells. after 4 days, there are 34 cells. how many cells will there be after seven days? a.149 b.120 c. 98 d.94

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

  D.  94

Welp life just is hard