A rumor about canceling spring break is being spread around a school.  The following equation models the number of students in the school who have heard the rumor after t days: N(t)=18001+149e−0.625t A.). How many people started the rumor? B. ). How many students are in the school? C.). To the nearest 1/10, how many days will it be before the rumor spreads to ½ the student body?

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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A rumor about canceling spring break is being spread around a school.  The following equation models the number of students in the school who have heard the rumor after t days:

N(t)=18001+149e−0.625t

A.). How many people started the rumor?

B. ). How many students are in the school?

C.). To the nearest 1/10, how many days will it be before the rumor spreads to ½ the student body?

D.). The following equation represents the instantaneous rate of change in students per day of the spread of the rumor. 

N1(t)=0.625N(1−N1800)

 

N represents the number of students who have heard the rumor and t is time in days. 

How many students have heard the rumor when the rumor is spreading the fastest? 

What is the rate of change in students per day at this time ?

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