Question

A country's population in 1992 was 28 million.

Answer 1

Answer:

The Estimate for the population in 2008 is 33 million

Step-by-step explanation:

Exponential Function

Some real-life situations can be modeled by using the exponential function which takes the form

$P = Ae^{kt}$

Where A and k are constants, and t is the independent variable.

We are given two data. A country's population in 1992 was 28 million and in 1999 it was 30 million.

Let's express P as the population in million and t the time in years elapsed since 1992.

The information can be written as two points: (0,28), (7,30). Please recall that the second data comes from the year 1999, seven years after the zero reference.

We only have to replace both points in the general form:

$28 = Ae^{k(0)}=A(1)=A$

We know A=28 million

Also

$30 = 28e^{k{(7)}}$

$28e^{7k}=30$

$\displaystyle e^{7k}=\frac{30}{28}$

Taking logarithms

$\displaystyle 7k=ln\left ( \frac{30}{28} \right )$

Solving for k

$\displaystyle k=\frac{ln\left ( \frac{30}{28} \right )}{7}$

$k=0.00986$

The model is complete now:

$P = 28e^{0.00986t}$

For the year 2008, t=2008-1992=16 years

$P = 28e^{0.00986(16)}$

$P = 28(1.1708)$

$P=32.78\ \approx 33$

The Estimate for the population in 2008 is 33 million