Questions: Partially because of people from a certain country living longer, the number with Alzheimer's disease and other dementia is projected to grow each year. The table below gives the millions of citizens in the country with Alzheimer's from 2000 and projected to 2050. Complete parts (a) through (e). Year 2000 2010 2020 2030 2040 2050 Number 3.9 5.7 6.9 8.9 11.6 14.3 Comment on the fit of the model on the data. Choose the correct answer below. A. The model is a good fit because it passes close to all of the data points. B. The model is a poor fit because it does not pass close to any of the data points. C. The model is an excellent fit because it passes through all of the data points. D. The model is a mediocre fit because it passes close to some of the data points.

Partially because of people from a certain country living longer, the number with Alzheimer's disease and other dementia is projected to grow each year. The table below gives the millions of citizens in the country with Alzheimer's from 2000 and projected to 2050. Complete parts (a) through (e).

Year 2000 2010 2020 2030 2040 2050
Number 3.9 5.7 6.9 8.9 11.6 14.3

Comment on the fit of the model on the data. Choose the correct answer below.
A. The model is a good fit because it passes close to all of the data points.
B. The model is a poor fit because it does not pass close to any of the data points.
C. The model is an excellent fit because it passes through all of the data points.
D. The model is a mediocre fit because it passes close to some of the data points.

Transcript text: Partially because of people from a certain country living longer, the number with Alzheimer's disease and other dementia is projected to grow each year. The table below gives the millions of citizens in the country with Alzhe from 2000 and projected to 2050. Complete parts (a) through (e). \begin{tabular}{lccc|c|c|c} Year & 2000 & 2010 & 2020 & 2030 & 2040 & 2050 \\ Number & 3.9 & 5.7 & 6.9 & 8.9 & 11.6 & 14.3 \end{tabular} Comment on the fit of the model on the data. Choose the correct answer below. A. The model is a good fit because it passes close to all of the data points. B. The model is a poor fit because it does not pass close to any of the data points. C. The model is an excellent fit because it passes through all of the data points. D. The model is a mediocre fit because it passes close to some of the data points.

Solution

Solution Steps

Step 1: Analyze the data and the models

The table shows a general upward trend in the number of citizens with Alzheimer's. We need to choose the model that best fits this trend.

Model A is a parabola opening upward. It suggests the number initially decreases, then increases.

Model B shows a continually decreasing trend.

Model C is a parabola opening downward. It suggests the numbers initially increase then decrease.

Model D displays a continually increasing trend.

Step 2: Eliminate unsuitable models

Models B and C clearly do not fit the upward trend shown in the table. Model A shows an initial decrease, which also doesn't match the data. Only Model D shows a continuously increasing trend, which is consistent with the data.

Step 3: Evaluate the fit of Model D

Model D is a linear, increasing function. While it doesn't pass exactly through every data point, it does come fairly close to each one.