The given quadratic function for the restaurant sales indicates that the sale first reduces then increases.
Reasons:
The function for the sales in the restaurant is y = 3·x² + 3.2·x + 514
Where;
y = Sales in billions of dollars
x = Number of years since 2008
Required:
The year in which the restaurant industry food and drink sales will be $1212 billion.
Solution:
When the food and drink sale is $1212 billion, we have;
1212 = 3·x² + 3.2·x + 514
Which gives;
3·x² + 3.2·x + 514 - 1212 = 0
3·x² + 3.2·x - 698 = 0
Factorizing with a graphing calculator gives;
(x + 15.796)·(x - 14.729) = 0
x = -15.796, or x = 14.729
The time will have a natural number value, therefore the positive value of x
= 14.729 is used.
Therefore, the number years since 2008 at which the restaurant sales will
be $1212 billion is approximately 15 years.
The year at which the sales will be $1212 billion = 2008 + 15 = 2023
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