Solve for t P=ae^(kt)

Problem

P=a*e^(k*t)

Solution

1. Isolate the exponential term by dividing both sides of the equation by a

P/a=e^(k*t)

2. Apply the natural logarithm to both sides of the equation to eliminate the base e

ln(P/a)=ln(e^(k*t))

3. Simplify the right side using the property ln(e^x)=x

ln(P/a)=k*t

4. Solve for t by dividing both sides by k

t=ln(P/a)/k

Final Answer

t=ln(P/a)/k

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