Question

The humidity is currently 56% and falling at a rate of 4 percentage points per hour. (a) Estimate the change in humidity over the next 20 minutes. (Round your answer to one decimal place.) -1.4 Incorrect: Your answer is incorrect. percentage points

Answer 1

Answer:

The change is of -1.3 percentage points.

Step-by-step explanation:

The humidity is currently 56% and falling at a rate of 4 percentage points per hour.

This means that after n hours the humidity is of:

$H(n) = 56 - 4n$

Estimate the change in humidity over the next 20 minutes.

It currently is 56%.

20 minutes is 20/60 = 1/3 of an hours, so:

$H(\frac{1}{3}) = 56 - 4\frac{1}{3} = 54.7$

Change:

54.7 - 56 = -1.3

The change is of -1.3 percentage points.

Answer 2

The change in humidity over the next 20 minutes falling at a rate of  4 percentage points per hour is -1.3.

The humidity is currently 56% and falling at a rate of 4 percentage points per hour.

What is the formula used to determine the change in humidity?

The change is determined by the small about of humidity changes x to x+h, so the output of x+h is the value of f at x plus the approximate change in f, that is

$\rm f(x+h) =f(x) + f'(x) \times h$

f(x)= 56%

20 minutes is 20/60 = 1/3 of an hours

So, The change in humidity is

$f'(x) = 4 \times 1/3$

f'(x) = 1.3

Here, it is falling at the rate of 4% point per hour so we will take it as negative as -1.3.

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