Question

. 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

Answer 1

Answer:)

a) f(t) = P₀ Rˣ

b) P (t) = 11,853 million

c) ˣ = 0,42 years

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