A graph of Q = 16e 0.18t is given in the figure. (a) What is the initial value of Q (when t= 0)? 16 Q(0) : * help (numbers) %3D 12 (b) This quantity decays at a continuous rate of % help (numbers) (c) Use the graph to estimate the value of t when Q = 4. help (numbers) (d) Use logs to find the exact value of t when Q = 4. help (logarithms) (Click on graph to enlarge)
A graph of Q = 16e 0.18t is given in the figure. (a) What is the initial value of Q (when t= 0)? 16 Q(0) : * help (numbers) %3D 12 (b) This quantity decays at a continuous rate of % help (numbers) (c) Use the graph to estimate the value of t when Q = 4. help (numbers) (d) Use logs to find the exact value of t when Q = 4. help (logarithms) (Click on graph to enlarge)
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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![A graph of \( Q = 16e^{-0.18t} \) is given in the figure.
**(a)** What is the initial value of \( Q \) (when \( t = 0 \))?
\[ Q(0) = \quad \text{help (numbers)} \]
**(b)** This quantity decays at a continuous rate of
\[ \quad \% \quad \text{help (numbers)} \]
**(c)** Use the graph to estimate the value of \( t \) when \( Q = 4 \).
\[ t \approx \quad \text{help (numbers)} \]
**(d)** Use logs to find the exact value of \( t \) when \( Q = 4 \).
\[ t = \quad \text{help (logarithms)} \]
**Graph Explanation:**
The graph is a plot of the function \( Q = 16e^{-0.18t} \). It shows an exponentially decaying curve starting at \( Q = 16 \) when \( t = 0 \). As \( t \) increases along the x-axis, \( Q \) decreases, approaching zero. Specific values, such as \( Q = 4 \), can be estimated by finding where the curve intersects the horizontal line at that value on the y-axis and matching it to the corresponding \( t \) value on the x-axis.
(Click on graph to enlarge)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74679fe8-edb8-480a-bbc2-dbd98253ae77%2Fc9065380-bdf6-4da0-935b-f13a1eafa1e9%2Frsmvndm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A graph of \( Q = 16e^{-0.18t} \) is given in the figure.
**(a)** What is the initial value of \( Q \) (when \( t = 0 \))?
\[ Q(0) = \quad \text{help (numbers)} \]
**(b)** This quantity decays at a continuous rate of
\[ \quad \% \quad \text{help (numbers)} \]
**(c)** Use the graph to estimate the value of \( t \) when \( Q = 4 \).
\[ t \approx \quad \text{help (numbers)} \]
**(d)** Use logs to find the exact value of \( t \) when \( Q = 4 \).
\[ t = \quad \text{help (logarithms)} \]
**Graph Explanation:**
The graph is a plot of the function \( Q = 16e^{-0.18t} \). It shows an exponentially decaying curve starting at \( Q = 16 \) when \( t = 0 \). As \( t \) increases along the x-axis, \( Q \) decreases, approaching zero. Specific values, such as \( Q = 4 \), can be estimated by finding where the curve intersects the horizontal line at that value on the y-axis and matching it to the corresponding \( t \) value on the x-axis.
(Click on graph to enlarge)
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