Studies show that the maximum half-life of Clonazepam is 50 hours. Use the following to construct a function that will model the maximum amount of Clonazepam left in the body after an initial dose of 45 mg. Q(t) = = Pe* Where Q(t) describes the amount of Clonazepam left in the body after t hours following an initial dose of P mg. 1. Q(t) = 2. How long (in hours) will it take for the amount of Clonazepam left in the body to reach 2 mg?
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![**Clonazepam Half-Life Study**
Studies show that the maximum half-life of Clonazepam is 50 hours.
**Objective:** Construct a function to model the maximum amount of Clonazepam left in the body after an initial dose of 45 mg.
The formula to use is:
\[ Q(t) = Pe^{rt} \]
Where \( Q(t) \) describes the amount of Clonazepam left in the body after \( t \) hours following an initial dose of \( P \) mg.
1. **Determine the Function:**
- **Q(t) =** [Input required]
2. **Calculate Time to Reach 2 mg:**
- How long (in hours) will it take for the amount of Clonazepam left in the body to reach 2 mg? [Input required]
**Note:** This exercise involves understanding the principles of exponential decay, using logarithms to solve for time, and applying the half-life formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5009a5f7-cb0c-44c8-a915-95d249ae3d2b%2F7eedd1e0-2fb7-4801-b278-991c4c303624%2Fnjspi9t_processed.png&w=3840&q=75)
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