Question
Asked By CrimsonShadow33 at
Answered By Expert
Benjamin
Expert Ā· 5.9k answers Ā· 5k people helped
Solution By Steps
Step 1: Initial Condition
Given
M(0) = 5.
Step 2: Differential Equation
The given differential equation is
\frac{dM}{dt} = \frac{1}{4}(40 - M).
Step 3: Slope at
(0,5)
Substitute
M = 5 into the differential equation to find the slope at
(0,5).
Step 4: Slope Field Interpretation
In the slope field, at
(0,5), the slope indicates the direction of the solution curve at that point.
Step 5: Sketching the Solution Curve
Follow the direction indicated by the slope field at
(0,5) to sketch the solution curve.
Final Answer
Sketch the solution curve starting at
(0,5) following the direction indicated by the slope field.
Key Concept
Slope Field Interpretation
Key Concept Explanation
Slope fields provide visual guidance on the direction of solution curves for differential equations at specific points. By following the slopes at given points, one can sketch the solution curve accurately.
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