SOLUTION: A lawyer has determined that the number of people P(t) in a city of 1.9 million people who have been exposed to a news item after t days is given by the function P(t) = 1,900,000(

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Question 1176907: A lawyer has determined that the number of people P(t) in a city of 1.9 million people who have been exposed to a news item after t days is given by the function
P(t) = 1,900,000(1 āˆ’ eāˆ’0.03t).
(a) How many days after a major crime has been reported has 20% of the population heard of the crime? (Round your answer to the nearest day.)
(b) A defense lawyer knows it will be difficult to pick an unbiased jury after 80% of the population has heard of the crime. After how many days will 80% of the population have heard of the crime? (Round your answer to the nearest day.)
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
380000=1900000(1-e^(-0.03t))
0.2=1-e^(-0.03t))
-0.8=-e^(-0.03t)
change both signs and take ln of both sides
-0.2231=-0.03t
t=7.4 days or 7 days
-
for 80%
0.2=e^(-0.03t)
-1.61=-0.03t
t=54 days
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