Question

The humidity is currently $32 \%$ and falling at a rate of 4 percentage points per hour. a. Estimate the change in humidity over the next 20 minutes. b. Estimate the humidity 20 minutes from now.

Name: Problem 1, Chapter 4: Calculus Concepts
Uploaded: 2021-12-06T18:12:14-08:00
Duration: 1 min 57 s
Channel: Gregory Higby
Description: The humidity is currently 32 % and falling at a rate of 4 percentage points per hour. a. Estimate the change in humidity over the next 20 minutes. b. Estimate the humidity 20 minutes from now.

   The humidity is currently $32 \%$ and falling at a rate of 4 percentage points per hour.
a. Estimate the change in humidity over the next 20 minutes.
b. Estimate the humidity 20 minutes from now.

Calculus Concepts

Donald R. LaTorre,… 5th Edition

Chapter 4, Problem 1

Instant Answer

Solved by Expert Gregory Higby

12/06/2021

Step 1

We need to find out how much it will fall in 20 minutes. Since there are 60 minutes in an hour, 20 minutes is one third of an hour. Therefore, the humidity will fall by one third of 4 percentage points in 20 minutes. Mathematically, this can be represented Show more…

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The humidity is currently $32 \%$ and falling at a rate of 4 percentage points per hour. a. Estimate the change in humidity over the next 20 minutes. b. Estimate the humidity 20 minutes from now.

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Key Concepts

Linear Extrapolation

Linear extrapolation involves extending a known rate of change to predict a future value of a quantity. Here, the assumption of a constant rate of change allows us to estimate the future humidity by applying the rate to the specified time interval, thereby approximating the new value based on current conditions.

Rate of Change

This concept refers to how a quantity changes over time, expressed as the amount of change per unit of time. In many practical problems, such as this one, the rate of change is assumed to be constant, allowing for straightforward calculations of how much a quantity will change over a different period.

Unit Conversion

Unit conversion is essential when dealing with quantities measured in different time units. In this context, converting hours to minutes (or vice versa) enables the use of a rate given per hour to calculate a change over a fraction of an hour, ensuring that the calculation remains consistent in terms of units.

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