REcall that we are given the price at 2003, which was 49. Note that at year 2004, there was an increase of 5% of 49. To calculate the 5% of a number, we simply multiply the number by 5 and divide it by 100. So, the price at year 2004 would be
[tex]49+\frac{5}{100}49[/tex]
Since we are told that each year there is a 5% increase of the initial price, this means that at year 2005 we would have another 5% extra. So the price at 2005 would be
[tex]49+\frac{5}{100}49+\frac{5}{100}49=49\cdot(1+2\cdot\frac{5}{100})[/tex]
Note that 2005 is 2 years after 2003, so, based on the pattern we are discovering in this formula, we can say that n years after 2003 the price would be
[tex]49\cdot(1+n\cdot\frac{5}{100})[/tex]
2014 is 11 years after 2003, so this means that n=11. If we replace the value of n, we have that the price at 2014 would be
[tex]49\cdot(1+11\cdot\frac{5}{100})=75.95[/tex]
so the price at year 2014 would be 75.95
