A grocery store receives a shipment of bananas. The percent of the shipment that is still suitable for sale is decreasing at a rate of r(t) percent of the original shipment per day (where t is the time in days). At t=2, the grocery store found 85% of the shipment to be suitable for sale. What does 0.85+int_(2)^(4)r(t)dt=0.6" mean? " Choose 1 answer: (A) Between the second and fourth day, another 60% of the bananas became unsuitable for sale. (B) Between the second and fourth days, 60% of the remaining bananas became unsuitable for sale per day. (C) As of the fourth day, 60% of the shipment was still suitable for sale. (D) As of the fourth day, 60% of the bananas suitable on the second day are still suitable.

Question

A grocery store receives a shipment of bananas. The percent of the shipment that is still suitable for sale is decreasing at a rate of  r(t) percent of the original shipment per day (where  t is the time in days). At  t=2, the grocery store found  85% of the shipment to be suitable for sale. What does  0.85+int_(2)^(4)r(t)dt=0.6" mean? " Choose 1 answer: (A) Between the second and fourth day, another  60% of the bananas became unsuitable for sale. (B) Between the second and fourth days,  60% of the remaining bananas became unsuitable for sale per day. (C) As of the fourth day,  60% of the shipment was still suitable for sale. (D) As of the fourth day,  60% of the bananas suitable on the second day are still suitable.

Bytelearn · Accepted Answer

Given Information: We are given that at t=2, 85% of the shipment is suitable for sale. The equation ＂0.85 + ∫_(2)^(4)r(t)dt = 0.6＂ includes an integral from t=2 to t=4, which represents the cumulative effect of the rate of decrease in suitability over these two days. The 0.85 at the beginning of the equation represents the 85% suitability at t=2.Integral Representation: The integral ∫_(2)^(4)r(t)dt represents the total percentage change in suitability from day 2 to day 4. Since r(t) is the rate of decrease per day, the integral sums up these rates over the interval from t=2 to t=4.Equation Interpretation: The equation is set equal to 0.6, which means that after adding the effect of the decrease from day 2 to day 4 to the initial suitability of 85%, the resulting suitability is 60%.Calculation Explanation: To interpret the equation, we need to understand that the 0.85 is not being added to the integral's result, but rather it is the starting value (85% suitable) which is being adjusted by the integral's result. The integral's result is the total percentage decrease over the two days, which when subtracted from the initial 85%, results in 60% suitability.Final Conclusion: Therefore, the correct interpretation of the equation is that as of the fourth day, 60% of the original shipment was still suitable for sale. This means that the answer is (C) As of the fourth day, 60% of the shipment was still suitable for sale.

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