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The adult population of a city is 1,150,000. A consultant to a law firm uses the function P(t)  1,150,000(1 – e–0.03t) to estimate the number of people P(t) who have heard about a major crime t days after the crime was first reported. About how many days does it take for 60% of the population to have been exposed to news of the crime?

Guest May 28, 2015

Best Answer 

 #1
avatar+78755 
+10

P(t) =  1,150,000(1 – e–0.03t)

 

60% of the population = 690,000  ...... so we have....

 

690,000 =   1,150,000(1 – e–0.03t)        divide both sides by 1,150,000

 

.60  = (1 - e^(-0.03t))   rearrange

 

.40  = e^(-0.03t)     take the ln of each side

 

ln .40  = ln e^(-0.03t)   and we can write

 

ln .40  = -.0.03t       divide both sides by -0.03

 

ln .40 / -0.03 = t = about 31 days

 

 

CPhill  May 28, 2015
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1+0 Answers

 #1
avatar+78755 
+10
Best Answer

P(t) =  1,150,000(1 – e–0.03t)

 

60% of the population = 690,000  ...... so we have....

 

690,000 =   1,150,000(1 – e–0.03t)        divide both sides by 1,150,000

 

.60  = (1 - e^(-0.03t))   rearrange

 

.40  = e^(-0.03t)     take the ln of each side

 

ln .40  = ln e^(-0.03t)   and we can write

 

ln .40  = -.0.03t       divide both sides by -0.03

 

ln .40 / -0.03 = t = about 31 days

 

 

CPhill  May 28, 2015

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