(3) As the salt KNO3 dissolves in methanol, the number r(t) of grams of the salt in a solution after t seconds satisfies the differential equation da/dt = 0.8 -0.004.2². (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If z=50 when t=0, how long will it take for an additional 50 g of salt to dissolve?
(3) As the salt KNO3 dissolves in methanol, the number r(t) of grams of the salt in a solution after t seconds satisfies the differential equation da/dt = 0.8 -0.004.2². (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If z=50 when t=0, how long will it take for an additional 50 g of salt to dissolve?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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HW5P3
![**Problem 3: Dissolving KNO₃ in Methanol**
As the salt \( KNO_3 \) dissolves in methanol, the number \( x(t) \) of grams of the salt in a solution after \( t \) seconds satisfies the differential equation:
\[
\frac{dx}{dt} = 0.8x - 0.004x^2
\]
**(a)** What is the maximum amount of the salt that will ever dissolve in the methanol?
**(b)** If \( x = 50 \) when \( t = 0 \), how long will it take for an additional 50 g of salt to dissolve?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3edbe93-d39c-43f4-8aa9-2c034a88e626%2F4219add6-9f07-4bfb-af71-dea0b88fb1c0%2F7zm76ql_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 3: Dissolving KNO₃ in Methanol**
As the salt \( KNO_3 \) dissolves in methanol, the number \( x(t) \) of grams of the salt in a solution after \( t \) seconds satisfies the differential equation:
\[
\frac{dx}{dt} = 0.8x - 0.004x^2
\]
**(a)** What is the maximum amount of the salt that will ever dissolve in the methanol?
**(b)** If \( x = 50 \) when \( t = 0 \), how long will it take for an additional 50 g of salt to dissolve?
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