SOLUTION: A lawyer has determined that the number of people P(t) in a city of 1.4 million people who have been exposed to a news item after t days is given by the function P(t) = 1,400,000(

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A lawyer has determined that the number of people P(t) in a city of 1.4 million people who have been exposed to a news item after t days is given by the function P(t) = 1,400,000(      Log On


   



Question 438613: A lawyer has determined that the number of people P(t) in a city of 1.4 million people who have been exposed to a news item after t days is given by the function
P(t) = 1,400,000(1 − e−0.03t).
How many days after a major crime has been reported has 35% of the population heard of the crime?
I tried -0.03t=ln 35/1400000

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P%28t%29+=+1400000%2A%281+-+e%5E%28-.03t%29%29+
given:
+P%28t%29+=+.35%2A1400000+
+P%28t%29+=+490000+
----------------
+490000+=+1400000%2A%281+-+e%5E%28-.03t%29%29+
+7%2F20+=+1+-+e%5E%28-.03t%29+
+-20%2F20+%2B+7%2F20+=+-e%5E%28-.03t%29+
+e%5E%28-.03t%29+=+65%2F100+
+ln%28e%5E%28-.03t%29%29+=+ln%28.65%29+
+-.03t+=+-.4308+
+t+=+14.36+
During the 15th day 35% have heard of the crime
check answer:
+P%28t%29+=+1400000%2A%281+-+e%5E%28-.03t%29%29+
+490000+=+1400000%2A%281+-+e%5E%28-.03%2A14.36%29%29+
+49%2F140+=+1+-+e%5E%28-.4308%29+
+7%2F20+=+1+-+.64999+
+.35+=+1+-+.65+
+.35+=+.35+
OK