Question

In​ 2012, the population of a city was 6.81 million. the exponential growth rate was 1.61​% 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.

Answer 1

For this case we have a function of the form:
y = A * (b) ^ t
Where,
A: initial amount
b: growth rate
t: time
For each of the questions we must make use of this equation in the following way:

Part A:
y = 6.81 * (1.0161) ^ t

Part B:
y = 6.81 * (1.0161) ^ 6
y = 7.49 million

Part C:
10 = 6.81 * (1.0161) ^ t
log1.0161 ((1.0161) ^ t) = log1.0161 ((10 / 6.81))
t = log1.0161 ((10 / 6.81))
t = 24.05 years

Part D:
2 * 6.81 = 6.81 * (1.0161) ^ t
log1.0161 ((1.0161) ^ t) = log1.0161 ((2 * 6.81 / 6.81))
t = log1.0161 (2)
t = 43.40 years