Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem 12**
We are given the function for quantity, \( q \), as:
\[ q = D(x) = 200e^{-0.05x} \]
where \( x = 80 \).
To solve this problem, we need to substitute \( x = 80 \) into the function to find the quantity \( q \).
**Steps:**
1. Substitute \( x = 80 \) into the equation:
\[ q = 200e^{-0.05 \times 80} \]
2. Calculate the exponent:
\[ -0.05 \times 80 = -4 \]
3. Substitute back into the equation:
\[ q = 200e^{-4} \]
4. Calculate the expression using \( e^{-4} \).
The final result will give you the value of \( q \) when \( x = 80 \).
This type of exponential function is often used in modeling growth or decay, such as in population dynamics, radioactive decay, or, in this scenario, a demand function which decreases at a certain rate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96e0847f-4973-4b99-ac1e-7e94417321c7%2F49fc99e2-7fbd-41ce-8c74-24577d4f753f%2F25wt8s_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 12**
We are given the function for quantity, \( q \), as:
\[ q = D(x) = 200e^{-0.05x} \]
where \( x = 80 \).
To solve this problem, we need to substitute \( x = 80 \) into the function to find the quantity \( q \).
**Steps:**
1. Substitute \( x = 80 \) into the equation:
\[ q = 200e^{-0.05 \times 80} \]
2. Calculate the exponent:
\[ -0.05 \times 80 = -4 \]
3. Substitute back into the equation:
\[ q = 200e^{-4} \]
4. Calculate the expression using \( e^{-4} \).
The final result will give you the value of \( q \) when \( x = 80 \).
This type of exponential function is often used in modeling growth or decay, such as in population dynamics, radioactive decay, or, in this scenario, a demand function which decreases at a certain rate.
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