Question

In​ 2012, the population of a city was 6.27 million. The exponential growth rate was 1.47​% per year.

Answer 1

Answer:

a) $a(t)= 6.27e^{0.0147*t}$

b) 6.84 million

c) 2028.52

d) 47 years

Step-by-step explanation:

a)Here we know standard exponential growth rate is

$a(t)= ae^{k*t}$

In this put t=0 and a(t)=6.27 million

thus we get a = 6.27 million

now $\frac{da}{dt}=a(t)k$

  this is equal to(in 2012)=$\frac{1.47}{100}*=0.0147$

b)Put t = 6

we get

$a(t)= 6.27e^{0.0147*6}$

=6.84 million

c) $8 = 6.27e^{0.0147*t}$

  take log both sides

we get 16.52 years

d) $2*6.27=6.27e^{0.0147*t}$

take log both sides we get 47 years to get double the current population.