The number of research articles in a prominent journal that were written by researchers in Europe can be modeled by P(t) = 1+5 4(1 21-t/2 Where t is time in years. The graphs of P, P', and P" are shown here. Graph of P Graph of P' P' 0.20 Graph of P" p" 0.010 6 5 0.15 0.005 4 0.10 3 0.000 10 20 30 40 0.05 -0.005 1 0.00 10 20 30 40 0 10 20 30 40 -0.010 Determine to the nearest whole number the values of t for which the graph of P is concave up and where it is concave down, and locate any points of inflection. concave up

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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7.0
The number of research articles in a prominent journal that were written by researchers in Europe can be modeled by P(t)
where t is time in years. The graphs of P, P', and P" are shown here.
1 + 5.4(1.2)-t/2'
Graph of P
Graph of P'
7
0.20
Graph of P"
6.
0.010
5
0.15
0.005
4
0.10
3
0.000
t
40
10
20
30
2
0.05
-0.005
0.00
10
20
30
40
10
20
30
40
-0.010
Determine to the nearest whole number the values of t for which the graph of P is concave up and where it is concave down, and locate any points of inflection.
concave up
<t<
concave down
<t<
point of inflection
t =
What does the point of inflection tell you about science articles?
From the graph of P' we see that P' has a maximum at around t =
meaning that the number of articles written by researchers in Europe was increasing most rapidly at around t =
Transcribed Image Text:7.0 The number of research articles in a prominent journal that were written by researchers in Europe can be modeled by P(t) where t is time in years. The graphs of P, P', and P" are shown here. 1 + 5.4(1.2)-t/2' Graph of P Graph of P' 7 0.20 Graph of P" 6. 0.010 5 0.15 0.005 4 0.10 3 0.000 t 40 10 20 30 2 0.05 -0.005 0.00 10 20 30 40 10 20 30 40 -0.010 Determine to the nearest whole number the values of t for which the graph of P is concave up and where it is concave down, and locate any points of inflection. concave up <t< concave down <t< point of inflection t = What does the point of inflection tell you about science articles? From the graph of P' we see that P' has a maximum at around t = meaning that the number of articles written by researchers in Europe was increasing most rapidly at around t =
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X - axis represent time and y axis represent prominent.

P is always increasing function domain t > 0

 

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