6. public awareness of a congressional candidate before and after a successful c

Question

6. public awareness of a congressional candidate before and after a successful campaign was approximated by P(t)= 8.4t/t^2+49 +0.1 0 < or equal to t < or equal to 24, where t is time in months after the campaign started and P(t) is the fraction of the number of people in the congressional district who could recall the candidate’s name. what is the average fraction of the number of people who could recall the candidate’s name during the first 7 months of the campaign? During the first 2 years of the campaign?

Explanation / Answer

Given P(t)= 8.4t/(t^2+49) +0.1 , 0<= t <= 24

average fraction of the number of people who could recall the candidate’s name during the

first 7 months of the campaign is

= 1/[7-0] 07 [8.4t/(t^2+49) +0.1 ]dt

=1/7 [ 07 4.2(2t)/(t^2+49)dt + 07 0.1 dt ]

=1/7 [ 4.2 ln(t^2+49) + 0.1t ]07

=1/7 [ 19.9569 - 16.3456 ]

= 0.5159

During the first 2 years of the campaign?

= 1/24 [ 024 4.2(2t)/(t^2+49)dt + 024 0.1 dt ]

=1/24 [ 4.2 ln(t^2+49) + 0.1t ]024

   = 1/24[ 29.4386- 16.3456 ]

=0.5456

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