Solve for t 6000=3000e^((0.04)(t))

Problem

6000=3000*e^(0.04*t)

Solution

1. Divide both sides of the equation by 3000 to isolate the exponential term.

2=e^(0.04*t)

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

ln(2)=ln(e^(0.04*t))

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

ln(2)=0.04*t

4. Solve for t by dividing both sides by 0.04

t=ln(2)/0.04

5. Calculate the numerical value.

t=25*ln(2)

t≈17.3287

Final Answer

t=ln(2)/0.04=25*ln(2)

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