Answer to Question #282115 in Differential Equations for Abdiqani

Question

Under certain conditions, cane sugar is converted into dextrose at a rate, which is proportional to the amount unconverted at any time. If out of 60 grams of sugar at t = 0 6 grams are converted during the first 4 minutes, find the amount converted in 2 hours.

Answer 1

$𝐶(𝑡) = 60 ⋅ ( 1 − 𝑒 ^{−𝑡⋅ln|( \frac{60 }{54}) ^\frac{1 }{4}|} ) = 60⋅ ( 1 − 𝑒^{ ln|( \frac{60 }{54}) −\frac{𝑡}{ 4}}| )$

$= 60 ⋅ (1 − ( \frac{60}{ 54})^\frac {−𝑡}{ 4})$

$C(120)= 60 ⋅ (1 − ( \frac{54}{ 60})^\frac {120}{ 4})=57.45g$