Given Data:

The exponential growth model is \(A=A_0e^{kt}\)

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 \(=A_0e^{k\times0}\)

\(A_0=110\) million

303 million \(A_0e^{k\times10}\)

303 million = 110 million\(\times e^{k\times10}\)

\(e^{10k}=2.75\)

\(10k=\ln2.75\)

\(k=0.101325\)

Thus, the required model equation is,

\(A=110e^{0.101325t}\)

The time after which the telephone users will be 400 million can be determined as,

\(400=110e^{0.101325t}\)

\(e^{0.101325t}=3.636\)

\(0.101325t=1.290\)

\(t=12.74\)

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.

The exponential growth model is \(A=A_0e^{kt}\)

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 \(=A_0e^{k\times0}\)

\(A_0=110\) million

303 million \(A_0e^{k\times10}\)

303 million = 110 million\(\times e^{k\times10}\)

\(e^{10k}=2.75\)

\(10k=\ln2.75\)

\(k=0.101325\)

Thus, the required model equation is,

\(A=110e^{0.101325t}\)

The time after which the telephone users will be 400 million can be determined as,

\(400=110e^{0.101325t}\)

\(e^{0.101325t}=3.636\)

\(0.101325t=1.290\)

\(t=12.74\)

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.