Since 2005, the amount of money spent at restaurants in a certain country has increased at a rate of 5% each year. . In 2005, about $570 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2014?
To solve the problem, we can use the formula for exponential growth:
A = P(1 + r)^t
where A is the amount of money spent at restaurants in a certain year, P is the initial amount spent in 2005, r is the annual growth rate (5%), and t is the number of years since 2005.
Using this formula, we can calculate the amount spent in 2014 as:
A = 570 billion(1 + 0.05)^9
A = 570 billion(1.638),
A ≈ 932.46 billion dollars
Therefore, about 932.46 billion dollars will be spent at restaurants in 2014 if the trend of 5% annual growth continues.
To calculate the amount that will be spent at restaurants in 2014, we need to determine the 10-year increase based on a 5% annual growth rate.
First, we calculate the increase in each year by multiplying the previous year's value by 5% (or 0.05):
Year 1 increase: $570 billion * 0.05 = $28.5 billion
Year 2 increase: ($570 billion + $28.5 billion) * 0.05 = $29.925 billion
Year 3 increase: ($570 billion + $28.5 billion + $29.925 billion) * 0.05 = $31.390625 billion
We continue this pattern for each year until we reach the 10th year.
Year 10 increase: ($570 billion + 9 previous years' increases) * 0.05 = $54.64608896 billion
Finally, we add the 10th-year increase to the initial amount spent in 2005:
Total amount spent in 2014 = $570 billion + $54.64608896 billion = $624.64608896 billion
Therefore, approximately $624.65 billion will be spent at restaurants in 2014 assuming the trend of 5% annual growth continues.