Question

The table shows population data for a community

Answer 1

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,

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

⇒ The predicted population in 2009 is approximately 124322.

Answer 2

It might have been 125,537.Hope that this help's you!!!!