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,
[tex]=\frac{\text{ Population in 2013 - Population in 2009 }}{\text{Population in 2009}}\times 100[/tex]
[tex]=\frac{138000-118000}{118000}\times 100[/tex]
[tex]=\frac{2000000}{118000}[/tex]
[tex]=16.9491525424\% \approx 16.94\%[/tex]
b) Let the function that shows the population after x years since 2007,
[tex]f(x)=ab^{x}[/tex]
Where a and b are any unknown number,
Since, for x = 0, f(0) = 118000 ( given)
⇒ [tex]118000 = ab^0[/tex]
⇒ [tex]a=118000[/tex]
Now, For x = 6, f(6) = 138,000 ( given )
⇒ [tex]138000 = ab^6[/tex]
⇒ [tex]138000= 118000 b^6[/tex]
⇒ [tex]b=1.0264382948[/tex]
Hence, the function that shows the population after x years since 2007,
[tex]f(x)=118000(1.0264382948)^{x}[/tex]
For, x = 2,
[tex]f(2)=118000(1.0264382948)^{2}=124321.917618\approx 124322[/tex]
⇒ The predicted population in 2009 is approximately 124322.
