Final answer:
To solve for t in the equation 2400=800e^(0.12*t), divide both sides of the equation by 800, take the natural logarithm of both sides, and divide by 0.12 to find that t is approximately 9.80 years.
Step-by-step explanation:
To solve for t in the equation 2400=800e^(0.12*t), we can start by dividing both sides of the equation by 800 to isolate the exponential term. This gives us 3=e^(0.12*t). To get rid of the exponential, we can take the natural logarithm (ln) of both sides of the equation. ln(3)=ln(e^(0.12*t)). Since ln(e^(0.12*t)) simplifies to 0.12*t, we have ln(3)=0.12*t. Finally, we can divide both sides of the equation by 0.12 to solve for t: t=ln(3)/0.12. Using a calculator, we can find that t is approximately 9.80 years.