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) As of the fourth day, 60% of the bananas suitable on the second day are still suitable. (B) Between the second and fourth days, 60% of the remaining bananas became unsuitable for sale per day. (C) Between the second and fourth day, another 60% of the bananas became unsuitable for sale. (D) As of the fourth day, 60% of the shipment was still suitable for sale.

Understand the expression: Understand the given expression. The expression ＂0.85 + ∫_(2)^(4)r(t)dt = 0.6＂ includes an integral, which represents the cumulative effect of the rate of decrease in suitability from day 2 to day 4. The 0.85 represents the 85% suitability on the second day, and the 0.6 represents the final suitability percentage on the fourth day.Interpret the integral: Interpret the integral part of the expression. The integral ∫_(2)^(4)r(t)dt represents the total percentage decrease in the suitability of the bananas from day 2 to day 4. This is added to the initial suitability percentage on the second day (85% or 0.85).Analyze the final value: Analyze the final value of the expression. Since the expression equals 0.6, this means that after adding the total percentage decrease from day 2 to day 4 to the initial 85% suitability, the final suitability percentage of the shipment is 60% on the fourth day.Match interpretation to answer: Match the interpretation to the answer choices. The correct interpretation of the expression is that as of the fourth day, 60% of the original shipment was still suitable for sale. This matches with answer choice (D).

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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. $\newline$ What does $0.85+\int_{2}^{4} r(t) d t=0.6 \text { mean? }$ $\newline$ Choose $1$ answer: $\newline$ (A) As of the fourth day, $60 \%$ of the bananas suitable on the second day are still suitable. $\newline$ (B) Between the second and fourth days, $60 \%$ of the remaining bananas became unsuitable for sale per day. $\newline$ (C) Between the second and fourth day, another $60 \%$ of the bananas became unsuitable for sale. $\newline$ (D) As of the fourth day, $60 \%$ of the shipment was still suitable for sale.

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Grade 7

Evaluate two-variable equations: word problems

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Q. 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.

\newline

What does

0.85+\int_{2}^{4} r(t) d t=0.6 \text { mean? }

\newline

Choose

1

answer:

\newline

(A) As of the fourth day,

60 \%

of the bananas suitable on the second day are still suitable.

\newline

(B) Between the second and fourth days,

60 \%

of the remaining bananas became unsuitable for sale per day.

\newline

60 \%

of the bananas became unsuitable for sale.

\newline

(D) As of the fourth day,

60 \%

of the shipment was still suitable for sale.

Understand the expression: Understand the given expression. $\newline$ The expression ＂ $0.85 + \int_{2}^{4}r(t)dt = 0.6$ ＂ includes an integral, which represents the cumulative effect of the rate of decrease in suitability from day $2$ to day $4$ . The $0.85$ represents the $85\%$ suitability on the second day, and the $0.6$ represents the final suitability percentage on the fourth day.
Interpret the integral: Interpret the integral part of the expression. $\newline$ The integral $\int_{2}^{4}r(t)\,dt$ represents the total percentage decrease in the suitability of the bananas from day $2$ to day $4$ . This is added to the initial suitability percentage on the second day ( $85\%$ or $0.85$ ).
Analyze the final value: Analyze the final value of the expression. $\newline$ Since the expression equals $0.6$ , this means that after adding the total percentage decrease from day $2$ to day $4$ to the initial $85\%$ suitability, the final suitability percentage of the shipment is $60\%$ on the fourth day.
Match interpretation to answer: Match the interpretation to the answer choices. $\newline$ The correct interpretation of the expression is that as of the fourth day, $60\%$ of the original shipment was still suitable for sale. This matches with answer choice $(D)$ .