Question

Week 1 2 3 4 5 Water Level (inches) − 1 1 4 1 3 8 2 1 2 − 1 5 8 − 1 3 4 Between which two weeks did the water level change the most? Calculate the change

Answer 1

The water level change the most in week 3 and week 4

The change = -370 inches

Explanation:

Given - Week 1 2 3 4 5

Water Level (inches) − 1 1 4 1 3 8 2 1 2 -1 5 8 -1 3 4

To find - Between which two weeks did the water level change the most? Calculate the change .

Proof -

The formula for change in water level with respect to week be-

Rate of Change in Water Level = Difference in water level / Difference in weeks

Now,

For week 1 and week 2

Rate of change in water level =
`(138 - 114)/(2 - 1)` =
`(24)/(1)` = 24 inches

Now,

For week 1 and week 3

Rate of change in water level =
`(212 - 114)/(3 - 1)` =
`(98)/(2)` = 49 inches

Now,

For week 1 and week 4

Rate of change in water level =
`(-158 - 114)/(4 - 1)` =
`-(272)/(3)` = -90.67 inches

Now,

For week 1 and week 5

Rate of change in water level =
`(-134 - 114)/(5 - 1)` =
`-(248)/(4)` = -62 inches

Now,

For week 2 and week 3

Rate of change in water level =
`(212 - 138)/(3 - 2)` =
`(74)/(1)` = 74 inches

Now,

For week 2 and week 4

Rate of change in water level =
`(-158 - 138)/(4 - 2)` =
`-(296)/(2)` = -148 inches

Now,

For week 2 and week 5

Rate of change in water level =
`(-134 - 138)/(5 - 2)` =
`-(272)/(3)` = -90.67 inches

Now,

For week 3 and week 4

Rate of change in water level =
`(-158 - 212)/(4 - 3)` =
`-(370)/(1)` = -370 inches

Now,

For week 3 and week 5

Rate of change in water level =
`(-134 - 212)/(5 - 3)` =
`-(346)/(2)` = 173 inches

Now,

For week 4 and week 5

Rate of change in water level =
`(-134 + 158)/(5 - 4)` =
`(24)/(1)` = 24 inches

∴ we get

The water level change the most in week 3 and week 4

The change = -370 inches

Note :

The highest change means which temperature goes the most change in water level. It can be negative also.

So, We have to take the modulus and then find the highest number.

Here, 370 > 173

So, Highest change occurs in Week 3 and Week 4 but not in Week 3 and Week 5.