See attached **Problem Statement:**A doctor prescribes 125 mg of a drug that decays by 30% per hour.**Part (b):** Write the formula for the decay of the drug in this form: $ f(t) = C \cdot e^{kt} $. Find the value for $ k $ rounded to six decimal places.**Explanation:**This problem involves calculating the decay constant $ k $ in the exponential decay formula. Exponential decay can be described using the formula $ f(t) = C \cdot e^{kt} $, where:- $ f(t) $ is the amount of drug remaining at time $ t $,- $ C $ is the initial amount of the drug,- $ k $ is the decay constant,- $ t $ is the time elapsed,- $ e $ is the base of the natural logarithm.The drug decays by 30% per hour, meaning if $ C = 125 $ mg initially, after one hour, 70% of it remains. Use this information to solve for $ k $.

Name: See attached **Problem Statement:**A doctor prescribes 125 mg of a dru
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Description: See attached **Problem Statement:**A doctor prescribes 125 mg of a drug that decays by 30% per hour.**Part (b):** Write the formula for the decay of the drug in this form: $ f(t) = C \cdot e^{kt} $. Find the value for $ k $ rounded to six decima

The amount of drug is 125 mg. The decaying rate is 30% per hour. Thus, the initial amount is C=125.…

Answered: (12) A doctor prescribes 125 mg of a…

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(12) A doctor prescribes 125 mg of a drug that decays by 30% per hour. Write the formula for the decay of the drug in this form: f(t) = C-e .Find the value for k (b) rounded to six decimal places.

Linear Algebra: A Modern Introduction

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See attached

**Problem Statement:**

A doctor prescribes 125 mg of a drug that decays by 30% per hour.

**Part (b):**
Write the formula for the decay of the drug in this form: $ f(t) = C \cdot e^{kt} $. Find the value for $ k $ rounded to six decimal places.

**Explanation:**

This problem involves calculating the decay constant $ k $ in the exponential decay formula. Exponential decay can be described using the formula $ f(t) = C \cdot e^{kt} $, where:
- $ f(t) $ is the amount of drug remaining at time $ t $,
- $ C $ is the initial amount of the drug,
- $ k $ is the decay constant,
- $ t $ is the time elapsed,
- $ e $ is the base of the natural logarithm.

The drug decays by 30% per hour, meaning if $ C = 125 $ mg initially, after one hour, 70% of it remains. Use this information to solve for $ k $.

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