Since 2004, the amount of money spent at restaurants in a certain country has increased at a rate of 7% each year. In 2004, about $290 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2018?

Guest Jun 13, 2021

#1**+2 **

In 2004 = $290 billion

In 2005 \(=(1+{7\over 100})*290\)

\(=310.3\)

In 2006 \(={107\over 100}×310.3\)

\(=332.02\)

In 2007 \(={107\over 100}×332.021\)

\(=355.26\)

... and so on

As you might have observed the above series forms a GP with

1st term **a _{1} = 290 **and common ratio

In order to find amount of money in 2018 (14 yrs later), we've to find the 15th term i.e. a

_{15}

⇒ \({a}_{15}= a × r^{14}\)

\(=290 × (10.7)^{14}\)

\(=$ 74777490355836152.54\) **billion** *(approx.) *

*~Hope you got it :) *

amygdaleon305 Jun 13, 2021