Question

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)=223(2.89)^t, where t = 0 corresponds to 2005. how many outlets were available in 2007, in 2009, in 2010? the number of outlets available in the year 2007 was approximately 1,863 (simplify your answer. round to the nearest integer as needed.) the number of outlets available in the year 2009 was approximately (simplify your answer. round to the nearest integer as needed.)

Explanation:

Step1: Determine \(t\) for 2009

Since \(t = 0\) corresponds to 2005, for 2009, \(t=2009 - 2005=4\).

Step2: Substitute \(t = 4\) into the formula

Substitute \(t = 4\) into \(A(t)=223(2.89)^{t}\), we get \(A(4)=223\times(2.89)^{4}\).
First, calculate \((2.89)^{4}=2.89\times2.89\times2.89\times2.89 = 67.652449\).
Then, \(A(4)=223\times67.652449\approx15086.5\).

Step3: Round the result

Round \(15086.5\) to the nearest integer, we get \(15087\).

Answer:

15087