Answer:
1. a) population of the town in 2024 = 8697
2.) the earthquake with a magnitude of 8 is a 100 times stronger than an earthquake with a magnitude of 6.
Step-by-step explanation:
1) the population of a town was, [tex]N_{0} = 7652[/tex] in 2016.
a) Exponential growth model is given by [tex]N(t) = N_{0} e^{kt}[/tex] where t is the time in years after 2016.
Year 2016 is when t = 0.
k = growth rate constant = 1.6% = 0.016
i) therefore the population of the town in 2024
= [tex]N = N_{0} e^{kt} = 7652e^{0.016\times8} = 8697[/tex] ( to the nearest whole number)
2.) log (I [tex]\times[/tex] M [tex]\times[/tex] S) = magnitude of earthquake where I is the Intensity of the earthquake and S is the intensity of a standard earthquake
therefore I [tex]\times[/tex] M [tex]\times[/tex] S = [tex]10^{magnitude\hspace{0.1cm}of\hspace{0.1cm}earthquake}[/tex]
therefore [tex]\frac{strength\hspace{0.1cm}of\hspace{0.1cm}earthquake\hspace{0.1cm}1 }{strength\hspace{0.1cm}of\hspace{0.1cm}earthquake\hspace{0.1cm}2} = \frac{10^{8} }{10^{6} } = 100[/tex]
