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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​? 

 Jun 13, 2021
 #1
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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 a1 = 290 and common ratio r = 10.7

 

In order to find amount of money in 2018 (14 yrs later), we've to find the 15th term i.e. a15 

⇒ \({a}_{15}= a × r^{14}\)

           \(=290 × (10.7)^{14}\)

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

 

 

 

~Hope you got it :) 

 Jun 13, 2021

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