The number of research articles in a prominent journal that were written by rese

Question

The number of research articles in a prominent journal that were written by researchers in Europe can be modeled by P(t) = 7.0 1 + 5.4(1.2)t where t is time in years. The graphs of P, P', and P'' are shown here. (Assume a = 4.)

Determine, to the nearest whole number, the values of t for which the graph of P is concave up, 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 =__________

O - N P A U ON 4a "O a 2a 2a 3a Graph of P 0.35% 0.3 0.25 0.2 0.15 0,1 0.05 a 2a 3a 4a Graph of P' 0.03% 0.02 0.01 2a 3a4a -0.01 -0.02 –0.03 Graph of P"

Explanation / Answer

concave up => P">0

concave up =>. 0<t<2.25a

concave up =>. 0<t<2.25*4

concave up => 0<t<9

concave down => P"<0

concave down =>. 2.25a<t<

concave down =>. 2.25*4<t<

concave down => 9<t<

point of inflection =(2.25a ,P(2.25a))

point of inflection =(9 ,3.4)

from the graph of P' we see that P' has a maximum at around t = 9:, meaning that the number of articles written by researchers in Europe was increasing most rapidly at around t =9

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