Question

The growth in the number (in millions) of Internet users in a certain country between 1990 and 2015 can be approximated by a logistic function with k 0.0014, where t is the number of years since 1990. In 1990 (when t 0), the number of users was about 3 million, and the number expected to level out around 220 million. (a) Find the growth function G(t) for the number of Internet users in the country. Estimate the number of Internet users in the country and the rate of growth for the following years. (b) 1994 (c) 2001 (d) 2010 (e) What happens to the rate of growth over time?

Answer 1

(a)

we can use logistics equation

y(t) Ae 1+Ae kt

we are given

k=0.0014

y(t) 1+Ae 0.0014t

at t=0 , y=3

we can use it

3 = 1+Ae 0.0014(0)

M 3 = 1A

at t=inf , y=220

220 1 Ae 0.0014x00

220 10

$M=220$

we can plug it

220 3 = 1A

217 A = 3

now, we can plug back it

and we get

220 G(t) 1217 e-0.0014t 3

(b)

In 1994:

t=1994-1990=4

we can plug it

220 G(4) 1217e-0.0014(4) 3

$G(4)=3.0166$

(c)

In 2001:

t=2001-1990=11

we can plug it

$G(11)=\frac{220}{1+\frac{217}{3}e^{-0.0014(11)}}$

$G(11)=3.04591$

(d)

In 2010:

t=2010-1990=20

we can plug it

$G(20)=\frac{220}{1+\frac{217}{3}e^{-0.0014(20)}}$

G 20) 3.08399