Public awareness of a congressional candidate before and after a successful camp

Question

Public awareness of a congressional candidate before and after a successful campaign was approximated by

P(t)= ((8.4t)/((t^2)+49))+0.1 where 0 is less than or equal to t which is less than or equal to 24

where t is time in months after the campaign started and P(t) is the fraction of people in the congressional district who could recall the candidate's name.

What is the average fraction of people who could recall the candidate's name during the first 7 months after campaign began?
What is the average fraction of people who could recall the candidate's name during the first 2 years after the campaign began?

Explanation / Answer

P(t)= ((8.4t)/((t^2)+49))+0.1 a).put t=7 in eqn P(7)=(8.4*7)/98 +0.1=0.7 thus average fraction of people who could recall the candidate's name during the first 7 months after campaign began=P(7)/7=0.7/7=0.1 b).put t=24 in the eqn P(24)=(8.4*24)/(625)+0.1=0.42 thus the average fraction of people who could recall the candidate's name during the first 2 years after the campaign began=P(24)/24=0.017

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