The circulation C of a certain magazine as a function of time t is given by the following formula.5.20.1 + 0.3Here Cis measured in thousands, and t is measured in years since the beginning of 2006, when the magazine was started.(a) Make the graph of C versus t covering the first 6 years of the magazine's existence.605050404030302020101012356.123466060505040403030202010F102345623456(b) Express using functional notation the circulation of the magazine 18 months after it was started.Find that value. (Round your answer to two decimal places.)thousand magazines(c) Over what time interval is the graph of C concave up?The graph of C is concave up from t =(smaller value) to t=(larger value) years.Explain what "concave up" means in practical terms.O The circulation was increasing more and more quickly.The circulation was decreasing more and more quickly.O The circulation was decreasing more and more slowly.O The circulation was increasing more and more slowly.(d) At what time was the circulation increasing the fastest? (Round your answer to the nearest year.)years(e) Determine the limiting value for C.C =|thousand magazinesExplain your answer in practical terms.O Itis the initial circulation.O Itis the level of market saturation.O It is the circulation with the highest growth rate.O It is the circulation att = 1.5.

(a) Given that, the function is C=5.20.1+0.3t Sketch the function C=5.20.1+0.3t as shown below,…

The circulation C of a certain magazine as a function of time t is given by the following formula. C- 5.2 0.1 + 0.3 Here Cis measured in thousands, and e is measured in years since the beginning of 2006, when the magazine was started. (a) Make the graph of C versus t covering the first 6 years of the magazine's existence. 6야 50 50 40 40 30 30 20 20 10 10 6아 60 5아 50 40 40 30 30 20 20 1아 1아 (6) Express using functional notation the circulation of the magazine 18 months after it was started. Find that value. (Round your answer to two decimal places.) ]thousand magazines (c) Over what time interval is the graph of C concave up? The graph of C is concave up from e = ( ](smaller value) to t = ( |(larger value) years. Explain what "concave up" means in practical terms. O The circulation was increasing more and more quickly. O The circulation was decreasing more and more quickly. O The circulation was decreasing more and more slowly. O The circulation was increasing more and more slowly.

The circulation C of a certain magazine as a function of time t is given by the following formula. C- 5.2 0.1 + 0.3 Here Cis measured in thousands, and e is measured in years since the beginning of 2006, when the magazine was started. (a) Make the graph of C versus t covering the first 6 years of the magazine's existence. 6야 50 50 40 40 30 30 20 20 10 10 6아 60 5아 50 40 40 30 30 20 20 1아 1아 (6) Express using functional notation the circulation of the magazine 18 months after it was started. Find that value. (Round your answer to two decimal places.) ]thousand magazines (c) Over what time interval is the graph of C concave up? The graph of C is concave up from e = ( ](smaller value) to t = ( |(larger value) years. Explain what "concave up" means in practical terms. O The circulation was increasing more and more quickly. O The circulation was decreasing more and more quickly. O The circulation was decreasing more and more slowly. O The circulation was increasing more and more slowly.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.3: Trigonometric Functions Of Real Numbers

Problem 67E

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The circulation C of a certain magazine as a function of time t is given by the following formula.
5.2
0.1 + 0.3
Here Cis measured in thousands, and t is measured in years since the beginning of 2006, when the magazine was started.
(a) Make the graph of C versus t covering the first 6 years of the magazine's existence.
60
50
50
40
40
30
30
20
20
10
10
1
2
3
5
6.
1
2
3
4
6
60
60
50
50
40
40
30
30
20
20
10F
10
2
3
4
5
6
2
3
4
5
6
(b) Express using functional notation the circulation of the magazine 18 months after it was started.
Find that value. (Round your answer to two decimal places.)
thousand magazines
(c) Over what time interval is the graph of C concave up?
The graph of C is concave up from t =
(smaller value) to t=
(larger value) years.
Explain what "concave up" means in practical terms.
O The circulation was increasing more and more quickly.
The circulation was decreasing more and more quickly.
O The circulation was decreasing more and more slowly.
O The circulation was increasing more and more slowly.
(d) At what time was the circulation increasing the fastest? (Round your answer to the nearest year.)
years
(e) Determine the limiting value for C.
C =
|thousand magazines
Explain your answer in practical terms.
O Itis the initial circulation.
O Itis the level of market saturation.
O It is the circulation with the highest growth rate.
O It is the circulation att = 1.5.

Expert Solution

Step 1

(a)

Given that, the function is $C = \frac{5.2}{0.1 + 0 . 3^{t}}$

Sketch the function $C = \frac{5.2}{0.1 + 0 . 3^{t}}$ as shown below,

From the above figure it is clearly observed that, the function is increasing on the interval (0,6).

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