Question

Rapunzel's hair is currently 110 inches long. She needs her hair to be at least 150 inches long in order to support a male suitor climbing it. She is currently using a magical conditioner that results in growth of 5% per week. A traveling witch offers to cast a spell on her hair that will result in growth of 7.5% per week, but will require her to trim 10 inches off in order for the spell to be effective . 1. Write an exponential function to represent the length of Rapunzel's hair after number of weeks if she continues to use the magical conditioner and doesn't take the witch's offer. 2. Write an exponential function to represent the length of Rapunzel's hair after x number of weeks if she lets the witch trim her hair and cast the spell 3. After four weeks, what will length of her hair be with each option ? Will her hair be long enough to supporta male suitor? 4. After six weeks what will the length of her hair be with each option? Should she let the witch cast her spell?

Answer 1

Explanation:

The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^ t

Where

y represents the length of the hair after t weeks.

t represents the number of weeks.

b represents the initial length of the hair.

r represents rate of growth.

1) When using the magical conditioner

b = 110 inches

r = 5% = 5/100 = 0.05

if she continues to use the magical conditioner and doesn't take the witch's offer, the exponential function would be

y = 110(1 + 0.05)^t

2) b = 110 - 10 = 100 inches

r = 7.5% = 7.5/100 = 0.075

The exponential function would be

y = 100(1 + 0.075)^x

3) when t = 4, for the first option,

y = 110(1 + 0.05)^4

y = 133.7 inches

when x = 4, for the second option,

y = 100(1 + 0.075)^4

y = 133.5 inches

Her hair will not be long enough for mail suitors to climb.

4) when t = 6, for the first option,

y = 110(1 + 0.05)^6

y = 147.4 inches

when x = 6, for the second option,

y = 100(1 + 0.075)^6

y = 154.3 inches

Yes, she should let the witch cast her spell.