MAT 121 HCC Linear & Exponential Connections Function Defining Algebra Worksheet

Can you answer the attached questions please. It is algebra and it is due tomorrow

MAT121
Name:___________________
Comparing Linear and Exponential Functions
An Austin area blog recently published an article stating “Based on the growth patterns from 2000 to 2012, our
findings are that the population of the Austin Metro Area will exceed the population of the New York Metro
Area by the year 2100.” (http://urbanscale.com/blog/austin-will-be-bigger-than-new-york-by-2100/)
The data that the blogger cited as his reasoning was the fact that in 2012 Austin had a population 0f 1.83 million
people and had been growing a steady 3.2% each year and that New York had 19.16 million people in 2012
and was increasing a steady 0.07 million people each year.
1. Let’s suppose for a few minutes that this information and the assumptions the blog writer used were true.
Use the information given to complete the tables below.
Years since
2012, t
Population of New York
Metro Area, N (in millions)
Years since
2012, t
0
0
1
1
2
2
3
3
4
4
Population of Austin
Metro Area, A (in millions)
2. a. Record the ways we “explain” each city’s rate of change with respect to time.
3. Because we don’t want to have to complete the table for 88 years (the year 2100), it would be useful to
create functions to model the populations of each city.
a. Define a function that gives the population of New York (in millions) with respect to t, the number of
years since 2012.
b. Define a function that gives the population of Austin (in millions) with respect to t, the number of years
since 2012.
Adapted from Bishop.
MAT121
Name:___________________
6. Use these functions to determine the population of each Metro Area in the year 2100. Given the
assumptions the blog writer made, are his conclusions correct?
Linear and Exponential Connections
Linear Relationships
Exponential Factors (b-values) and Percent Rates
Adapted from Bishop.
Exponential Relationships