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The function is , where represents the number of years since from .
(a). Graph of the function .
In this case represents the number of years since from , so graph of the function is valid only positive values of .
(b). Estimate the number of alternative-fueled vehicles in use in the United States in .
The year represents .
Estimate graphically:
The number of alternative-fueled vehicles were there in the United States in the year is .
Confirm algebraically:
Substitute in .
.
The number of alternative-fueled vehicles were there in the United States in the year is .
(c). Observe the graph:
End behavior of the graph : .
It appears that as the number of years after increases without bound, the number of alternative-fueled vehicles increases without bound. Due to money and space constraints, infinitely many alternative-fueled vehicles cannot exist.
Therefore, the model is not valid for all years after .
(a). Graph of the function is,
(b). vehicles.
(c). It appears that as the number of years after increases without bound, the number of alternative-fueled vehicles increases without bound. Due to money and space constraints, infinitely many alternative-fueled vehicles cannot exist.
Therefore, the model is not valid for all years after .
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