In 2012 the population of a city was 579 million The exponen

In 2012, the population of a city was 5.79 million. The exponential growth rate was 2.81% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 10 million? d) Find the doubling time. a) The exponential growth function is P(t) =, where t is in terms of the number of years since 2012 and P(t) is the population in millions. (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

Solution

Dear Student Thank you for using Chegg !! Given Data Population in 2012 = 5.79 Million Exponential growth rate = 2.81% per year Exponential growth function should be P(t) = P(0)e^0.0281t where t is number of years passed since 2012 = 5.79e^0.0281t Million b) Population in 2018 t = 6 years = 5.79e^0.0281*6 = 6.853313731 6.85 Million c) P(t) = 10 Million => 10 = 5.79e^0.0281t Taking natural log both sides 2.302585093 = ln(5.79) + 0.0281t 0.546452801 = 0.0281t t = 19.44671891 years i.e. in year 2031 d) Doubming Time P (t) = 2 P(0) 2P(0) = P(0) e^0.0281t 2 = e^0.0281t Taing natural log both sides 0.693147181 = 0.0281t t = 24.66715945 Hence the popultion will double in 2037