ANSWER
a). T = 493 (rounded to nearest whole number)
b). n = 6 years (rounded to nearest whole number)
EXPLANATION
Given:
[tex]T=280\times1.12^n[/tex]
Desired Outcome:
1. Number of Taxis (T) at the end of 2005
2. n (in years) when T is doubled
Number of Taxis (T) at the end of 2005
[tex]\begin{gathered} T\text{ = 280}\times1.12^5 \\ T=280\times1.7623 \\ T=493.455 \end{gathered}[/tex]
Number of years
[tex]\begin{gathered} T\text{ = 280}\times2=560 \\ 560=280\times1.12^n \\ 1.12^n=\frac{560}{280} \\ 1.12^n=2 \\ log1.12^n=log2 \\ nlog1.12=0.3010 \\ n=\frac{0.3010}{0.0492} \\ n=6.117 \end{gathered}[/tex]
Hence, number of Taxis (T) at the end of 2005 is 493 (rounded to nearest whole number) and the year in which the taxis is doubled is 6 (rounded to nearest whole number) .
