Question

1) The population of a town was7652in 2016. The population grows at a rate of 1.6%annually.(a)Use the exponential growth model to write an equation that estimates the population t years after 2016.(a)Estimate the population of the town in 2024. Show your work.
2)The formula logIMS=determines the magnitude of an earthquake, where Iis the intensity of the earthquake and Sis the intensity of a “standard earthquake.”How many times stronger is an earthquake with a magnitude of 8 than an earthquake with a magnitude of 6? Show your work

Answer 1

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, $N_{0} = 7652$ in 2016.

a) Exponential growth model is given by $N(t) = N_{0} e^{kt}$ 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

    = $N = N_{0} e^{kt} = 7652e^{0.016\times8} = 8697$   ( to the nearest whole number)

2.) log (I $\times$ M $\times$ S) = magnitude of earthquake  where I is the Intensity of the earthquake and S is the intensity of a standard earthquake

therefore  I $\times$ M $\times$ S = $10^{magnitude\hspace{0.1cm}of\hspace{0.1cm}earthquake}$

therefore $\frac{strength\hspace{0.1cm}of\hspace{0.1cm}earthquake\hspace{0.1cm}1 }{strength\hspace{0.1cm}of\hspace{0.1cm}earthquake\hspace{0.1cm}2} = \frac{10^{8} }{10^{6} } = 100$