How to do fractions
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Answer:
At what time will 90% of the population have heard the rumor?
The rumor was heard by 90% of the population in 5.9 hours or 5 hours and 54 minutes
So, at 1:54 pm, 90% of the population had heard the rumor.
Step-by-step explanation:
To resolve this exercise we need to know the exponential model:
(1)
Where:
the quantity inhabitants in certain time who heard the rumor
Initial people who heard the rumor
k: constant
t: time frame
We know in 4 hours ( hours) half the town has heard the rumor because:
inhabitants
With this information we can find the constant (k), because we have all the information in
400 people
120 people
t= 4 hours
When we replace in equation 1 we have:
We multiply by natural logarithm on both sides of this equation and we have:
With the constant (k) we can find at what time 90% of the population have heard the rumor
(90% of the population)
So we have:
720 people
120 people
When we replace in equation 1 we have:
We multiply by natural logarithm on both sides of this equation and we have:
We can find how many minutes are 0.9 hours:
t= 5 hours and 54 minutes
Now, we know the rumor was heard by 90% of the population in 5.9 hours or 5 hours and 54 minutes
So, at 1:54 pm, 90% of the population had heard the rumor.