Question

The function$$D(h)=5 e^{-0.4 h}$$can be used to find the number of milligrams $D$ of a certain drug that is in a patient's bloodstream $h$ hours after the drug was administered. When the number of milligrams reaches $2,$ the drug is to be administered again. What is the time between injections?

Name: Problem 125, Chapter 6: Algebra and Trigonometry
Uploaded: 2021-05-22T08:20:47-08:00
Duration: 2 min 30 s
Channel: Swati Agarwal
Description: The functionD(h)=5 e^-0.4 hcan be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug was administered. When the number of milligrams reaches 2, the drug is to be administered again. What is the time between injections?

   The function$$D(h)=5 e^{-0.4 h}$$can be used to find the number of milligrams $D$ of a certain drug that is in a patient's bloodstream $h$ hours after the drug was administered. When the number of milligrams reaches $2,$ the drug is to be administered again. What is the time between injections?

Algebra and Trigonometry

Michael Sullivan 11th Edition

Chapter 6, Problem 125

Instant Answer

Solved by Expert Swati Agarwal

05/22/2021

Step 1

4 h}$ and we know that the drug is to be administered again when $D(h) = 2$. So, we substitute $D(h) = 2$ into the function to find the value of $h$. Show more…

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The function$$D(h)=5 e^{-0.4 h}$$can be used to find the number of milligrams $D$ of a certain drug that is in a patient's bloodstream $h$ hours after the drug was administered. When the number of milligrams reaches $2,$ the drug is to be administered again. What is the time between injections?

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Key Concepts

Solving Exponential Equations

Solving exponential equations involves the use of logarithms to isolate the variable in the exponent. This method is essential when determining time or other unknowns in contexts modeled by exponential growth or decay, by converting the exponential relationship into a linear equation.

Natural Logarithm

The natural logarithm is the logarithm with base e and plays a crucial role in solving equations involving exponential functions. It allows one to 'bring down' the exponent, turning multiplicative relationships into additive ones, which simplifies the process of isolating variables.

Exponential Decay

Exponential decay describes a process where a quantity decreases at a rate proportional to its current value. It is typically modeled with functions that include a constant factor multiplied by an exponential term with a negative exponent, indicating the rate of decay over time.

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