Question

This has many steps and I do appreciate you helping me with this problem.

Answer 1

a). T = 493 (rounded to nearest whole number)

b). n = 6 years (rounded to nearest whole number)

Step-by-step explanation

Given:

`T=280*1.12^n`

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

`\begin{gathered} T\text{ = 280}*1.12^5 \\ T=280*1.7623 \\ T=493.455 \end{gathered}`

Number of years

`\begin{gathered} T\text{ = 280}*2=560 \\ 560=280*1.12^n \\ 1.12^n=(560)/(280) \\ 1.12^n=2 \\ log1.12^n=log2 \\ nlog1.12=0.3010 \\ n=(0.3010)/(0.0492) \\ n=6.117 \end{gathered}`

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) .