In 2012, the population of a city was 6.56 million. the continuous growth rate was 3.49% per year. a) find the exponential growth function for the population t years after 2012. b) estimate the population of the city in 2018. c) when will the population of the city be 11 million

)

a) f(t)  = P₀ Rˣ

b) P (t)   = 11,853  million

c) ˣ =  0,42 years  

Step-by-step explanation:

a)

The exponential growth function for population is:

f(t)  = P₀ Rˣ

Where  f(t)  is population at t

P₀  = population at t= 0

R growth rate

x = t = time

b) For  2018,  6 years after  2012     t = 6

P (t)   =  6,56 * (3,49)⁶     ⇒   P (t)   = 6,56* 1807

P (t)   = 11,853  million

c) When will the population of the city be 11 million

11  = 6,56* (3,49)ˣ     ⇒  1,68 =  (3,49)ˣ

Taking log both sides of the equation

log (1,68)  =  ˣ * log (3,49)

ˣ =  0,42 years