To find the total capacity of the storage container, we need to determine how much fertilizer is deposited over the entire period of time.
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Initial deposits: In the first 5 weeks, the farm deposits 1.5 ft³ of fertilizer each week. Therefore, in 5 weeks, the total amount deposited is: \[ 1.5 , \text{ft}^3/\text{week} \times 5 , \text{weeks} = 7.5 , \text{ft}^3 \]
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Fertilizer after 5 weeks: According to the problem, after 5 weeks, the container has 15 ft³ of fertilizer.
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Fertilizer added after 5 weeks: Since the container has 15 ft³ after the first 5 weeks, and we've calculated that 7.5 ft³ was added during that time, we can infer that there was already an initial amount of fertilizer in the container before the deposits started. We can calculate that initial amount (I) as follows: \[ I + 7.5 , \text{ft}^3 = 15 , \text{ft}^3 \] Rearranging gives us: \[ I = 15 , \text{ft}^3 - 7.5 , \text{ft}^3 = 7.5 , \text{ft}^3 \]
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Deposits after 5 weeks: For the next 14 weeks, the farm continues to deposit fertilizer at the same rate of 1.5 ft³ per week. The total added during these 14 weeks is: \[ 1.5 , \text{ft}^3/\text{week} \times 14 , \text{weeks} = 21 , \text{ft}^3 \]
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Total fertilizer in the container: Now, we calculate the total amount of fertilizer in the container at the end of this period: \[ \text{Total} = \text{Initial amount} + \text{Amount after 5 weeks} + \text{Amount after 14 weeks} \] Substituting in the values we calculated: \[ \text{Total} = 7.5 , \text{ft}^3 + 15 , \text{ft}^3 + 21 , \text{ft}^3 = 43.5 , \text{ft}^3 \]
Therefore, the capacity of the storage container is 43.5 ft³.
The answer is D. 43.5 ft³.
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