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The amount of gasoline stored at a fuel station is decreasing at a rate of r(t) liters per hour (where t is the time in hours). What does int_(20)^(21)r(t)dt=-450 mean? Choose 1 answer: (A) During the 20^("th ") hour, the amount of gasoline at the fuel station decreased by 450 liters. (B) During the first 20 hours, the amount of gasoline at the fuel station decreased by 450 liters. (C) During the first 21 hours, the amount of gasoline at the fuel station decreased by 450 liters. (D) During the 21^("st ") hour, the amount of gasoline at the fuel station decreased by 450 liters.

The amount of gasoline stored at a fuel station is decreasing at a rate of r(t) r(t) liters per hour (where t t is the time in hours).\newlineWhat does ∫2021r(t)dt=−450 \int_{20}^{21} r(t) d t=-450 mean?\newlineChoose 11 answer:\newline(A) During the 20th  20^{\text {th }} hour, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(B) During the first 2020 hours, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(C) During the first 2121 hours, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(D) During the 21st  21^{\text {st }} hour, the amount of gasoline at the fuel station decreased by 450450 liters.

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Q. The amount of gasoline stored at a fuel station is decreasing at a rate of r(t) r(t) liters per hour (where t t is the time in hours).\newlineWhat does ∫2021r(t)dt=−450 \int_{20}^{21} r(t) d t=-450 mean?\newlineChoose 11 answer:\newline(A) During the 20th  20^{\text {th }} hour, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(B) During the first 2020 hours, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(C) During the first 2121 hours, the amount of gasoline at the fuel station decreased by 450450 liters.\newline(D) During the 21st  21^{\text {st }} hour, the amount of gasoline at the fuel station decreased by 450450 liters.
  1. Understand expression: Understand the integral expression.\newlineThe integral expression ∫2021r(t) dt\int_{20}^{21} r(t) \, dt represents the total change in the amount of gasoline at the fuel station from hour 2020 to hour 2121.
  2. Interpret negative sign: Interpret the negative sign. The negative sign in front of 450450 indicates that the amount of gasoline is decreasing. Therefore, the integral tells us that there is a decrease in the amount of gasoline.
  3. Determine time interval: Determine the time interval.\newlineThe integral limits are from 2020 to 2121, which means we are looking at the change during the 21st21^{\text{st}} hour, not the cumulative change over the first 2020 or 2121 hours.
  4. Match interpretation: Match the interpretation with the answer choices.\newlineThe correct interpretation is that during the 21st21^{\text{st}} hour, the amount of gasoline at the fuel station decreased by 450450 liters. This matches with choice (D).

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