Question

19 select the correct answer from each drop - down menu. the table shows the population of a small but growing town from the time it was incorporated. year 0 1 2 3 4 5 6 7 8 population of town 1,500 1,655 1,800 2,001 2,185 2,416 2,640 2,935 3,250 this data can be modeled with an exponential function. the equation of the curve of best fit is y = 1,495.3·1.1^x. the correlation coefficient is 0.9997. complete the sentences to describe the model. based on the curve of best fit, the town had approximately people when it was incorporated, and the population grew around % each year. there is association between time and the towns population because the correlation coefficient is

Explanation:

Step1: Find initial - population

The exponential function is $y = 1495.3\times1.1^{x}$, when $x = 0$ (the year of incorporation), $y=1495.3\times1.1^{0}=1495.3\approx1495$.

Step2: Find the growth - rate

For an exponential function $y = a\times b^{x}$, the growth rate $r$ is given by $b = 1 + r$. Here $b = 1.1$, so $r=b - 1=1.1-1 = 0.1$ or $10\%$.

Step3: Analyze the correlation - coefficient

The correlation coefficient $r = 0.9997$. Since $r$ is very close to $1$, there is a strong positive linear association between time and the town's population.

Answer:

1. 1495
2. 10
3. a strong positive