Answer:  a) 16.9491525424 %

b)  124322 ( approx )

Step-by-step explanation:

a) The population in 2009 = 118000

While the population in 2013 = 138,000

Thus, the total percentage change in the population from 2009 to 2013,

=frac{text{ Population in 2013 - Population in 2009 }}{text{Population in 2009}}times 100

=frac{138000-118000}{118000}times 100

=frac{2000000}{118000}

=16.9491525424% approx 16.94%

b) Let the function that shows the population after x years since 2007,

f(x)=ab^{x}

Where a and b are any unknown number,

Since, for x = 0, f(0) = 118000 ( given)

118000 = ab^0

a=118000

Now, For x = 6, f(6) = 138,000 ( given )

138000 = ab^6

138000= 118000 b^6

b=1.0264382948

Hence, the function that shows the population after x years since 2007,

f(x)=118000(1.0264382948)^{x}

For, x = 2,

f(2)=118000(1.0264382948)^{2}=124321.917618approx 124322

The predicted population in 2009 is approximately 124322.