Nadia Saba
11/12/23 9:12 PM
Question 4, 5.2.63
HW Score: $50 \%, 2$ of 4 points
Part 2 of 3
Points: 0 of 1
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The total number of public electric charging units available for hybrid vehicles has increased exponentially since 2006 . The number of outlets $A(t)$ at these alternative fueling stations $t$ years after 2006 can be approximated by $A(t)=230(2.84)^{t}$, where $t=0$ corresponds to 2006 . How many outlets were available in 2008 , in 2010 , in 2011 ?
The number of outlets available in the year 2008 was approximately 1855 . (Simplify your answer. Round to the nearest integer as needed.)
The number of outlets available in the year 2010 was approximately $\square$. (Simplify your answer. Round to the nearest integer as needed.)
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Answer
The number of outlets available in the year 2010 was approximately \(\boxed{14962}\).
Step 1 ：The question is asking for the number of outlets available in the year 2010. We can use the given formula \(A(t)=230(2.84)^{t}\) to calculate this. Here, \(t\) is the number of years after 2006. So for the year 2010, \(t\) would be 4. We can substitute \(t=4\) into the formula and calculate the result.
Step 2 ：Substitute \(t=4\) into the formula \(A(t)=230(2.84)^{t}\).
Step 3 ：Calculate \(A(4) = 230(2.84)^{4}\).
Step 4 ：The number of outlets available in the year 2010 was approximately \(\boxed{14962}\).
