Use the exponential growth model A=A_0e^{kt} to solve: In 2000, there were 110 million cellphone subscribers in the United States. By 2010, there were

EunoR 2021-03-08 Answered
Use the exponential growth model A=A0ekt to solve: In 2000, there were 110 million cellphone subscribers in the United States. By 2010, there were 303 million subscribers
a. Find the exponential function that models the data.
b. According to the model, in which year were there 400 million cellphone subscribers in the United States?
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Expert Answer

funblogC
Answered 2021-03-09 Author has 91 answers

Given Data:
The exponential growth model is A=A0ekt
In 2000 the number of telephone users was 110 million.
In 2010 the number of telephone users was 303 million.
Taking 2000 as the base year (t=0) and A as the number of cellphone users then, boundary condition can be written as,
t=0,A=110 million
t=10,A=303 million
Substituting the boundary condition in the model equation,
101 million =A0ek×0
A0=110 million
303 million A0ek×10
303 million = 110 million×ek×10
e10k=2.75
10k=ln2.75
k=0.101325
Thus, the required model equation is,
A=110e0.101325t
The time after which the telephone users will be 400 million can be determined as,
400=110e0.101325t
e0.101325t=3.636
0.101325t=1.290
t=12.74
Thus, the year in which the number of telephone users will be 400 million is
2000+12.74=2012.74
Thus, in the year 2013 the number of telephone users will be 400 million.

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