Question

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.)

Answer 1

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