The total number of public electric charging units available for hybrid vehicles has increased exponentially since 
2005
2005. The number of outlets​ A(t) at these alternative fueling stations t years after 
2005
2005 can be approximated by 
Upper A left parenthesis t right parenthesis equals 222 left parenthesis 2.74 right parenthesis Superscript t
A(t)=222(2.74)t​, where t
equals
=0 corresponds to 
2005
2005. How many outlets were available in 
2007
2007​, in 
2009
2009​, in 
2010
2010​?

The function \( A(t) = 222 \times 2.74^t \) gives the number of public electric charging outlets \( A(t) \) at time \( t \) years after 2005. To find the number of outlets in 2007, 2009, and 2010, we calculate \( A(t) \) for the respective values of \( t \).

1. **For 2007**:  
   Since 2007 is 2 years after 2005, \( t = 2 \).  
   \[
   A(2) = 222 \times 2.74^2
   \]
   
2. **For 2009**:  
   Since 2009 is 4 years after 2005, \( t = 4 \).  
   \[
   A(4) = 222 \times 2.74^4
   \]
   
3. **For 2010**:  
   Since 2010 is 5 years after 2005, \( t = 5 \).  
   \[
   A(5) = 222 \times 2.74^5
   \]

Let me calculate these values.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you’d like to continue manually, here’s what you can do:

1. For 2007: Plug \( t = 2 \) into the formula and calculate \( A(2) = 222 \times 2.74^2 \).
2. For 2009: Plug \( t = 4 \) into the formula and calculate \( A(4) = 222 \times 2.74^4 \).
3. For 2010: Plug \( t = 5 \) into the formula and calculate \( A(5) = 222 \times 2.74^5 \).

Feel free to reach out again if you'd like help with more calculations or details!

Here are 5 follow-up questions:
1. How do exponential growth models apply to other types of infrastructure, like solar power stations?
2. What factors contribute to the rapid increase in electric charging stations?
3. Could other functions (e.g., linear or logarithmic) model this situation more accurately at some point?
4. What is the significance of the base (2.74) in the given formula?
5. How might future technologies affect the rate of increase for charging stations?

**Tip:** When dealing with exponential growth, even small changes in the base can result in significant differences over time!

The total number of public electric charging units available for hybrid vehicles has increased exponentially since 2005. The number of outlets​ A(t) at these alternative fueling stations t years after 2005 can be approximated by A(t)=222(2.74)^t, where t=0 corresponds to 2005. How many outlets were available in 2007, 2009, and 2010?

Explore the exponential growth in public electric charging outlets since 2005 using the formula A(t) = 222(2.74)^t. This problem covers exponential growth concepts in algebra and models real-world increases in electric charging stations for hybrid vehicles. Suitable for students in Grades 9-12.

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