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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