Let's begin by analyzing the information given in the problem:
- The farm deposits \(1.5f \cdot t^3\) of fertilizer into the storage container each week.
- After 5 weeks, the total amount of fertilizer in the container is \(15f \cdot t^3\).
- It takes 14 more weeks for the storage container to be filled.
First, we need to calculate how much fertilizer is deposited in the first 5 weeks:
\[ \text{Fertilizer deposited in 5 weeks} = 5 \times (1.5f \cdot t^3) = 7.5f \cdot t^3 \]
According to the problem, the total amount in the container after 5 weeks is \(15f \cdot t^3\). Therefore, we can set up an equation that accounts for the accumulation:
\[ \text{Initial amount in container} + \text{Amount deposited in 5 weeks} = \text{Total after 5 weeks} \]
Let \(C\) be the initial amount of fertilizer in the container:
\[ C + 7.5f \cdot t^3 = 15f \cdot t^3 \]
Now, subtract \(7.5f \cdot t^3\) from both sides to find \(C\):
\[ C = 15f \cdot t^3 - 7.5f \cdot t^3 = 7.5f \cdot t^3 \]
Now we know that the initial amount in the container is \(7.5f \cdot t^3\).
Next, we need to determine how much more fertilizer is added over the next 14 weeks:
\[ \text{Fertilizer deposited in 14 weeks} = 14 \times (1.5f \cdot t^3) = 21f \cdot t^3 \]
Now, let's calculate the total amount of fertilizer in the storage container after the additional 14 weeks:
\[ \text{Total amount in container} = \text{Initial amount} + \text{Amount deposited in 5 weeks} + \text{Amount deposited in 14 weeks} \]
Substituting in the values:
\[ \text{Total amount} = 7.5f \cdot t^3 + 7.5f \cdot t^3 + 21f \cdot t^3 \]
Simplifying this gives:
\[ \text{Total amount} = 7.5f \cdot t^3 + 7.5f \cdot t^3 + 21f \cdot t^3 = 36f \cdot t^3 \]
Therefore, the total capacity of the storage container is:
\[ \text{Capacity of the storage container} = 36f \cdot t^3 \]
Now we can compare this to the answer choices provided. The capacity does not match any of the exact formats given (A, B, C, D). However, if we need to express this in terms of what may be the closest valid choice:
If we investigate the choices:
- A: 21f * t^3
- B: 8.36f * t^3
- C: 0.28 * 0.5f * t^3 = 0.14f * t^3
- D: 43.5f * t^3
Since \(36f \cdot t^3\) is not exactly equal to any of the values, it appears that we may need to reaffirm if \(36f \cdot t^3\) was split between the amounts after the 14 weeks. Therefore, None of the options given stands as the right total capacity conclusion or adjustment.
Hence, if \(36f \cdot t^3\) is required in the context of the problem to get the nearest surplus from the given choices, no option is completely valid compared to \(36f \cdot t^3\). Since \(36f \cdot t^3\) is also not reconcilable directly with provided choices numerically, the capacity of the storage container is therefore inferred to be \(36f \cdot t^3\).