At the beginning of 1990, 21.7 million people lived in the metropolitan area of a particular city, and the population was growing exponentially. the 1996 population was 25 million. if this trend continues, how large will the population be in the year 2010

approximately 27.5 million

Step-by-step explanation:

If 1990 is the initial year, we will rename it as 0.  This is the x coordinate in a pair we will need to write the equation that models this particular situation.  The y coordinate that goes along with it is 21.7 (x is time in years, y is number of people).  The next coordinate pair we have is (6, 25).  If 1990 is year 0, 1996 is year 6.  

The standard form for an exponential equation is

where y is the number of people, x is the number of years gone by, a is the initial value, and b is the growth rate.  We fill in equation 1 with the x and y coordinates from coordinate pair (0, 21.7):

andything rised to the power of 0 = 1, so b raised to 0 = 1:

21.7 = a(1) so

a = 21.7

Now we use coordinate pair (6, 25) in equation 2, subbing in our value for a also:

Divide both sides by 21.7 to get

We "undo" that power of 6 by taking the 6th root of both sides:

That gives you that

b = 1.0238 (rounded).

Now that we have a and b, we can write the model for this situation:

Now that we have the model, we can find y when x = 10 (2010):

First raise 1.0238 to the 10th power to get

y = 21.7(1.266097) and

y = 27.47