Question

Below are two tables based on the actual populations of Raleigh, NC and Wake County, NC from 1920-1990. Using Excel, create separate tables for t versus p for the Raleigh and Wake County data. (Note: Some of these values are randomized and may not exactly match the data you have seen in the lesson.)

Years since 1900	Raleigh Population (in thousands)
20	24
30	37.3
40	46.8
50	65.6
60	93.9
70	122
80	150
90	212

Years since 1900	Wake County Population (in thousands)
20	75.1
30	94.7
40	109
50	136
60	169
70	228
80	301
90	423

For the Raleigh data, use Trendline to find the best fit of the exponential model. (Give all answers correct to at least two decimal places.)

The growth rate is  %.

The population in 1900 was ____ thousand people.

The population in 2010 was ____thousand people.

The population in 2100 will be____ thousand people.

How long after 1900 did the population reach 100,000?
_______ years

For the Wake County data, use Trendline to find the best fit of the exponential model. (Give all answers correct to at least two decimal places.)

The growth rate is ______ %.

The population in 1900 was _____ thousand people.

The population in 2010 was ______thousand people.

The population in 2100 will be_____ thousand people.

c. According to your fits of this data to exponential models, which is projected to have a larger population in 2100? (You have only one attempt. Please use your submission wisely.)

Raleigh or Wake County   

d. This result doesn't make sense. Why? (Select all that apply.)

1. The data could be wrong.

2. The parameters fitting the exponential model could be wrong.

3. The exponential model might not be the best model to describe these two populations.

4. Using 70 years of data to project 110 years ahead is absurd.

5. The city can't physically be larger than the county.

d. Log-transform the data for Raleigh. (Give your answer correct to at least four decimal places.)
R² =  

e. This means which of the following is true? (You have only two submissions. Please use them wisely.)

Raleigh's population was growing exactly linearly 1920 - 1990.

Raleigh's population was growing close to linearly 1920 - 1990.    

Raleigh's population was growing exactly exponentially 1920 - 1990.

Raleigh's population was growing close to exponentially 1920 - 1990.

Raleigh's population met all the assumptions for exponential growth 1920 - 1990.

Answer 1