a.
To write: A model giving the population
The population in 2000 is 664.284 thousands.
Given:
The population of Austin in 1990 is 494,290.
The population is increased by 3% per year for the next 10 years.
Calculation:
Here, the initial population is
The growth rate is,
Now the model is,
Now since 10 years after 1990 is 2000, therefore to find the population in 2000, put
Hence, the population in 2000 is 664.284 thousands.
b.
To find: The given model and to estimate when the value of the car will be $10,000.
The domain is
Given:
Calculation:
The given function passes through the points
Now the graph is,
From the graph, it can be seen that the time is ranging from
So, the domain is
The population is ranging from 494.29 thousands to 664.284 thousands.
So, the range is
c.
To find: The year in which the population is 590,000.
The population is 590,000 in the year 1996.
Given:
Calculation:
By substituting
Therefore, the population is 590,000 in about 6 years after 1990.
Hence, the population is 590,000 in the year 1996.
Chapter 4 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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