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Exponential and Logarithmic Functions - Sketching Exponential Functions and Solving Equations Graphically

Exponential and Logarithmic Functions - Sketching Exponential Functions and Solving Equations Graphically

IP 3

Sketch \(y=\frac{4}{{{\mathrm{e}}^{2x}}}\). Hence find the equation of the straight line which must be added on the graph of \(y=\frac{4}{{{\mathrm{e}}^{2x}}}\) to solve the equation \(\ln 4-2x=\ln \left( 4+3x \right)\).

Solution:

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Answer:Sketch \(y=4\mathrm e^{-2x}\) with intercept \((0,4)\) and asymptote \(y=0\). Add \(y=4+3x\); the intersection is at \((0,4)\).

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