write and graph a function that represents the situation

Question

write and graph a function that represents the situation, a population of 15,000 increases by 8.5% each year

Answer 1

Population after 1 year = 15000 + (0.085)(15000)

 

                                          = 15000(1 + 0.085) = 15000(1.085)

 

Population in 2 years = Population after 1 year + 8.5% of that

 

                                      = 15000(1.085) + 0.085[15000(1.085)]

 

                                      = 15000(1.085)(1 + 0.085)

 

                                      = 15000(1.085)²  

 

Population in t years = 15000(1.085)^t

 

 

 

 

 

Answer 2

Since the population increases, we have an exponential growth function.  The population starts at 15000.

 

y = 15000e^0.085x

 

where:

y = population

x = time in years