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)=233(2.87)ᵗ, where t=0 corresponds to 2005. How many outlets were available in 2007, in 2009, and in 2010?

Answer 1

To find the number of outlets available in 2007, 2009, and 2010, substitute the corresponding values of t into the equation a(t)=233(2.87)ᵗ. For 2007, there were approximately 1919 outlets. For 2009, there were around 6530 outlets. For 2010, there were approximately 18666 outlets.

Step-by-step explanation:

To find the number of outlets available in 2007, 2009, and 2010, we need to substitute the corresponding values of t into the equation a(t)=233(2.87)ᵗ.

For 2007, t=2 since it is 2 years after 2005. So, a(2) = 233(2.87)² = 233(2.87)(2.87) = 233(8.2369) ≈ 1919 outlets.

For 2009, t=4 since it is 4 years after 2005. So, a(4) = 233(2.87)⁴ = 233(2.87)(2.87)(2.87)(2.87) = 233(28.035897) ≈ 6530 outlets.

For 2010, t=5 since it is 5 years after 2005. So, a(5) = 233(2.87)⁵ = 233(2.87)(2.87)(2.87)(2.87)(2.87) = 233(80.1323343) ≈ 18666 outlets.