Respuesta :
Answer:
[tex]N(t)=22.76(1.0081)^t[/tex]Explanation:
The exponential function is of the form:
[tex]N(t)=a(b)^t[/tex]In 2004, (i.e. t=0), the number of licensed drivers = 22.76 million
[tex]\begin{gathered} N(t)=22.76,t=0 \\ 22.76=a(b)^0 \\ \implies a=22.76 \end{gathered}[/tex]In 2009, the number of licensed drivers = 23.7 million
[tex]\begin{gathered} a=22.76,N(t)=23.7,t=2009-2004=5 \\ N(t)=a(b^t)\implies23.7=22.76(b)^5 \end{gathered}[/tex]We solve for the value of b:
[tex]\begin{gathered} 23.7=22.76(b)^5 \\ b^5=\frac{23.7}{22.76} \\ b=\sqrt[5]{\frac{23.7}{22.76}} \\ b=1.0081 \end{gathered}[/tex]Therefore, an exponential formula for the number, N, of licensed drivers in the US as a function of t, the numbers of years since 2004 is:
[tex]N(t)=22.76(1.0081)^t[/tex]Note: N(t) is in millions
