Complete an equation for the number of restaurants per capita (per person)

Question

The population of a town has been growing, following the equation P = 300 t + 7000, where t is years after 2010. The number of restaurants in the town has been growing according to the equation R = 4 t + 25.

 

How many restaurants per capita does this model predict for the year 2015?

Answer 1

t is the time since 2010, so

 

the population prediction for 2015 is:

  P = 300(2015-2010) + 7,000 

  P = 300(5) + 7,000 = 8,500

 

the number of restaurants prediction for 2015 is:

  R = 4(2015-2010) + 25

  R = 4(5) + 25   = 45

 

So per capita (per person) there would be:

  45 Restaurants for 8,500 People that is:  45/8500

  or  0.00529  restaurants per person   <------

 

  per restaurant there would be:  8500/45

  or 188.89 persons per restaurant       <------

Answer 2

Sha,

 

Restaurants per capita (t) = # restaurants / population, corresponding to time t

                                      = [R/P] = [(4t + 25) / (300 t + 7000)]  , where t = 2015 - 2010 = 5 years

                                      = [45 / 8500] = 0.00529  

Answer 3

restaurants per capita = R/P

R/P = (4t + 25) / (300t + 7000)

t = 2015 - 2010

t = 15

 

R/P = (4 · 15 + 25) / (300 · 15 + 7000)

R/P = 85 / (4500 + 7000)

R/P = 85 / 11500

R/P = 0.000739