Question

A student cuts pieces of ribbon to decorate a banner the first piece of ribbon is 24 inches long. The next piece of ribbon is one-half the length of the piece before, and so on. What is the total length of the first 6 pieces of ribbon?
A) 0.75
B) 1.5
C) 23.25
D) 47.25

Answer 1

Answer:

Option D) 47.25 in

Step-by-step explanation:

we know that

The equation of a exponential decay function is equal to

$y=a(1-r)^x$

where

y is the total length

x is the number of pieces of ribbon

a is the initial value

r is the rate of change

we have

$a=24\ in\\r=50\%=50/100=0.50$

substitute

$y=24(1-0.50)^x$

$y=24(0.50)^x$

we have that

For x=0 ----->$y=24\ in$

For x=1 ----> $y=24(0.50)^1=12\ in$

For x=2 ----> $y=24(0.50)^2=6\ in$

For x=3 ---->$y=24(0.50)^3=3\ in$

For x=4 ----> $y=24(0.50)^4=1.5\ in$

For x=5 ----> $y=24(0.50)^5=0.75\ in$

Adds the length of the first 6 pieces of ribbon

$24+12+6+3+1.5+0.75=47.25\ in$