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 withk=0.0016where t is the number of years since 1990. In 1990​ (whent=​0),the number of users was about44​million, and the number is expected to level out around220million.​(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?​(a)​ G(t)equals=(INSERT ANSWER HERE)

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Asked Mar 7, 2020
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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=0.0016
where t is the number of years since 1990. In 1990​ (when
t=​0),
the number of users was about
44
​million, and the number is 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?
​(a)
​ G(t)equals=(INSERT ANSWER HERE)
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Expert Answer

Step 1

The logistic function is given as,

Calculus homework question answer, step 1, image 1,

where G0=initial number

m= maximum possible number

t=time

k=constant

Step 2

(a) In the given problem, 

G0=44 million

m  = 220 million

k= 0.0016

plugging all these vlaues in the logistic function,

Calculus homework question answer, step 2, image 1

(b) in year 1994,

t=4 years, ( since stating year is 1990)

plugging t=4 in G(t),

Calculus homework question answer, step 2, image 2

(c) in year 2001,

t=11 years

Calculus homework question answer, step 2, image 3

(d) in year 2010,

t=20 years,

Calculus homework question answer, step 2, image 4

(e) From the above cases, we see that as the year goes up, the growth rate increases.

 

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