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In 2000 the total amount of gamma ray bursts was recorded at 6.4 million for a city. In 2005, the same survey was made and the total amount of gamma ray bursts was 7.3 million. If the Earth can only withstand 1 billion gamma ray bursts, in what year will this become a problem? (Find the year in which the gamma ray bursts is 1 billion.)

1 Answer

3 votes

Let's assume

It started in 2000

so, t=0 in 2000


P_0=6.4million

we can use formula


P(t)=P_0 e^(rt)

we can plug value


P(t)=6.4 e^(rt)

In 2005, the same survey was made and the total amount of gamma ray bursts was 7.3 million

so, at t=2005-2000=5

P(t)=7.3 million

we can plug value and then we can solve for r


7.3=6.4 e^(r*5)


r=0.02632

now, we can plug back


P(t)=6.4 e^(0.02632t)

now, we have

P(t)=1 billion =1000 million

so, we can set it and then we can solve for t


1000=6.4 e^(0.02632t)


t=191.924

approximately


t=192

Year is 2000+192

year is 2192................Answer

User Keet Sugathadasa
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