Total Number of Orders Gia Bao's Catering Company Plans to Fulfill
How many orders in total does Gia Bao’s company plan to fulfill by the end of the first year? Is this realistic?
For each month afterward, Gia Bao wants the company to double the number of orders than the previous month. How many orders in total does Gia Bao’s company plan to fulfill by the end of the first year? Is this realistic?
Final answer:
To find the total number of orders Gia Bao's company plans to fulfill by the end of the first year, we need to calculate the sum of all the orders for each month. Using the formula for the sum of a geometric sequence, we can find the total number of orders for the first year.
Explanation:
To find the total number of orders Gia Bao's company plans to fulfill by the end of the first year, we need to calculate the sum of all the orders for each month. In the first month, there are 12 orders. For each month afterward, the number of orders doubles. So, the second month will have 2 * 12 = 24 orders, the third month will have 2 * 24 = 48 orders, and so on.
We can see that the number of orders in each month forms a geometric sequence. Using the formula for the sum of a geometric sequence, we can find the total number of orders for the first year. The formula is:
S = a * (r^n - 1) / (r - 1)
Where S is the sum, a is the first term, r is the common ratio, and n is the number of terms. In this case, a = 12, r = 2, and n = 12 (since there are 12 months in a year).
Plugging these values into the formula, we get:
S = 12 * (2^12 - 1) / (2 - 1)
Simplifying this expression gives us the total number of orders Gia Bao's company plans to fulfill by the end of the first year.