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Answer:
Step-by-step explanation:
From the given information:
Given that the solution is pumped at a slower rate of 4gal/min
Then:
The differential equation can be expressed as:
Integrating the linear differential equation; we have::
multiplying above integrating factor fields; we have:
A = (50 + t) + c(50 + t)²
Using the given conditions:
A(0) = 20
⇒ 20 = 50 + c (50)⁻²
-30 = c(50) ⁻²
c = -30 × 2500
c = -75000
A = (50+t) - 75000(50 + t)⁻²
The no. of pounds of salt in the tank after 35 minutes is:
A(35) = (50 + 35) - 75000(50 + 35)⁻²
A(35) = 85 -
A(35) =69.6193 pounds
A(35) 70 pounds
Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.