suppose that a new company that makes yo yos made 560 yoyos the first week the company overestimated its requirements. The managements intends to decrease the number of yoyo how the company will manufacture by 8 percent each week for 8 week.
The number of yo-you that the company can be represented by a geometric sequence
How many yo-yos will the company manufacture in 8 weeks?
a = 560
r = 1-0.8 = 0.92
...
To find the number of yo-yos the company will manufacture in 8 weeks, we need to use the given information that the company will decrease the number of yo-yos by 8 percent each week.
First, let's find the number of yo-yos manufactured in the first week which is 560.
Now, we can use the formula for a geometric sequence to find the number of yo-yos manufactured in each subsequent week.
The formula for a geometric sequence is:
an = a * r^(n-1)
Where:
an = the nth term of the sequence
a = the first term of the sequence
r = the common ratio (percentage decrease expressed as a decimal)
n = the number of terms in the sequence (number of weeks)
In this case, the first term (a) is 560 and the common ratio (r) is 0.08 (8 percent decrease expressed as a decimal).
To find the number of yo-yos manufactured in 8 weeks, we substitute these values into the formula:
a8 = 560 * 0.08^(8-1)
Now we can calculate the answer:
a8 = 560 * 0.08^7
a8 ≈ 267.53
Therefore, the company will manufacture approximately 267 yo-yos in 8 weeks.