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