The population of a city for years since 2000 is shown below. Which kind of function best models the data? Write an equation to model the data.
To find : Which type of function best model the given data, use differences or ratio.
Answer to Problem 26P
Exponential model is the most appropriate model and the equation to model the data is
Explanation of Solution
Given information :
The population of a city for years since 2000 is shown in table
Calculation :
To find the type of model from the given set of data use the followings:
- If the first difference of the y values is common, then linear model fits the data
- If the second difference of the y values is common, then quadratic model fit the data.
- If the y values have the common ratio, then an exponential model fits he data.
For the given set of data, find the find difference of the y values:
Since, the first differences is not common, so find the second differences
Since, the second differences are also not common, so find the ratio of the y values.
Since, y values have the common ratio. Therefore, exponential model is the most appropriate model.
Let the exponential model be
Substitute
Substitute
Therefore, the equation is
Hence,
Exponential model is the most appropriate model and the equation to model the data is
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