When sugar is dissolved in water, the amount A that remains undissolved after t minutes satisfie

Name: When sugar is dissolved in water, the amount A that remains undissolved after t minutes satisfies the differential equation d A / d t=-k A(k>0) . If 25 % of the sugar dissolves after 1 min, how long does it take for half of the sugar to dissolve?
Uploaded: 2021-12-19T03:56:09-08:00
Duration: 2 min 48 s
Channel: Ma. Theresa Alin
Description: When sugar is dissolved in water, the amount A that remains undissolved after t minutes satisfies the differential equation d A / d t=-k A(k>0) . If 25 % of the sugar dissolves after 1 min, how long does it take for half of the sugar to dissolve?

Question

Ma. Theresa Alin · Accepted Answer

Step 1: Start with the differential equation given: $frac{dA}{dt} = -kA$

Question

When sugar is dissolved in water, the amount $A$ that remains undissolved after $t$ minutes satisfies the differential equation $d A / d t=-k A(k>0) .$ If $25 \%$ of the sugar dissolves after 1 min, how long does it take for half of the sugar to dissolve?

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