Final answer:
To solve the equation 10 = 20e^-0.0001216t for t, we need to isolate e^-0.0001216t, take the natural logarithm of both sides, and then divide by the coefficient of t. Negative time solutions are considered non-physical and discarded.
Step-by-step explanation:
The original equation given is 10 = 20e^-0.0001216t. To solve for t, we first need to isolate the exponential term by dividing both sides by 20 to get 0.5 = e^-0.0001216t.
Taking the natural logarithm ln of both sides gives us ln(0.5) = -0.0001216t. Finally, dividing both sides by -0.0001216 yields t = ln(0.5) / -0.0001216. Plugging this into a calculator will give us a positive value for t.
It is important to note here that a negative value for time is not physical as it would imply that the event happened before it started, which in real-world scenarios is not possible. Therefore, negative time solutions are discarded.