MATH SOLVE

3 months ago

Q:
# 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 sequenceHow many yo-yos will the company manufacture in 8 weeks?

Accepted Solution

A:

Answer:312 yoyos in 8th week; 3407 yoyos over 8 weeks
Step-by-step explanation:The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
In your geometric sequence, a₁ = 560 and r = 0.92.
Thus, the formula for your sequence is
aₙ = 560(0.92)ⁿ⁻¹
Eighth term
a₈ = 560(0.92)⁷ = 560 × 0.5578 = 312
The company will manufacture 312 yoyos in the eighth week.
Sum over eight weeks
The formula for the sum of the first n terms of a geometric series is
Sum = a₁[(1 - rⁿ)(1 - r)]
Sum = 560[(1 - 0.92⁸)/(1 - 092)] = 560[(1 - 0.513 22)/0.08 ] = 560 × (0.486 78/0.08) = 560 × 6.0848 = 3407
The company will manufacture a total of 3407 yoyos over eight weeks.