/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 110 The average temperature for Bost... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 110

The average temperature for Boston in January 2005 was 43 "F. In 2007 the average January temperature was \(44.5^{\circ} \mathrm{F}\). What is the rate of change of the temperature per year? If this trend continues, what is the expected average temperature in January \(2010 ?\)

Short Answer

Expert verified
The rate of change is \(0.75^{\circ} \mathrm{F/year}\), and the expected average temperature in January 2010 is \(46.75^{\circ} \mathrm{F}\).

Step by step solution

01

Understanding Rate of Change

The rate of change tells us how much the temperature changes per year. To find it, we'll calculate how much the temperature changed from 2005 to 2007, and then divide by the number of years in that period.
02

Calculating the Temperature Change

First, find the difference in temperatures between the two given years: \[ 44.5^{\circ} \mathrm{F} - 43^{\circ} \mathrm{F} = 1.5^{\circ} \mathrm{F} \]So, the temperature increased by \(1.5^{\circ} \mathrm{F}\) from 2005 to 2007.
03

Determining the Number of Years

Next, calculate the number of years between 2005 and 2007: \[ 2007 - 2005 = 2 \]Thus, there are 2 years between 2005 and 2007.
04

Calculating the Rate of Change

Now, divide the change in temperature by the number of years to find the rate of change:\[ \text{Rate of Change} = \frac{1.5^{\circ} \mathrm{F}}{2 \text{ years}} = 0.75^{\circ} \mathrm{F/year} \]This means the temperature increased by \(0.75^{\circ} \mathrm{F}\) per year.
05

Projecting Temperature for 2010

To find the temperature for 2010, calculate the number of years from 2007 to 2010:\[ 2010 - 2007 = 3 \]Multiply the number of years by the rate of change:\[ 3 \times 0.75^{\circ} \mathrm{F/year} = 2.25^{\circ} \mathrm{F} \]Add this increase to the 2007 temperature to find the 2010 temperature:\[ 44.5^{\circ} \mathrm{F} + 2.25^{\circ} \mathrm{F} = 46.75^{\circ} \mathrm{F} \]Thus, the expected average temperature in January 2010 is \(46.75^{\circ} \mathrm{F}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Temperature Change
When discussing temperature change, especially over several years, it's important to know how to measure this variation accurately. Temperature change is simply the difference between two temperature readings taken at two different points in time.
For instance, in Boston, the average temperature in January 2005 was 43掳F, and it rose to 44.5掳F in 2007.
This means there was an increase in temperature by:
  • 44.5掳F (in 2007) - 43掳F (in 2005) = 1.5掳F
This positive change signifies that the temperature is increasing. Temperature change can be a crucial indicator when examining climate patterns over time. It helps us see if a specific area is experiencing warming or cooling trends.
Calculating Average Temperature
Average temperature gives us a snapshot of overall climate conditions for a specific time and location.
It is calculated by taking several temperature readings over a period and finding their mean value. In this exercise, though, we deal with given averages for specific years, so no calculations of daily temperatures are needed.
Instead, we use the provided average for each year (2005 and 2007) to determine the trend, such as the rate of change. Understanding the average temperature is vital because:
  • It helps in assessing climate norms.
  • It offers a basis for comparing different years.
By examining these annual averages, we can detect if a warming or cooling trend is becoming evident, which is essential in making climate-related decisions and analyses.
Projecting Future Temperature
Projecting future temperature involves using past trends to estimate what might occur in the future. It's like forecasting the weather, but on a longer time scale.
To project the future temperature based on previous trends:
  • Start with identifying the rate of change, which is the average change per year.
  • This rate is then multiplied by the number of years into the future you are projecting.
  • Add this product to the temperature of the last known year to get the projected temperature.
In our case, the rate of change was found to be 0.75掳F per year. To predict the temperature in 2010, calculate for the 3 years since 2007:
  • 0.75掳F/year 脳 3 years = 2.25掳F increase.
Adding this to the 2007 temperature (44.5掳F) gives an estimated average of 46.75掳F in January 2010.
This approach provides a valuable insight into how temperatures may change if current trends continue. However, keep in mind that actual future conditions can be influenced by various unforeseen factors.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Refer to the following: Einstein's special theory of relativity states that time is relative: Time speeds up or slows down, depending on how fast one object is moving with respect to another. For example, a space probe traveling at a velocity \(v\) near the speed of light \(c\) will have "clocked" a time \(t\) hours, but for a stationary observer on Earth that corresponds to a time \(t_{0} .\) The formula governing this relativity is given by $$ t=t_{0} \sqrt{1-\frac{v^{2}}{c^{2}}} $$ If the time elapsed on a space probe mission is 5 years but the time elapsed on Earth during that mission is 30 years, how fast is the space probe traveling? Give your answer relative to the speed of light.

A speedboat takes 1 hour longer to go 24 miles up a river than to return. If the boat cruises at 10 mph in still water, what is the rate of the current?

Find the equation of the line that passes through the given point and also satisfies the additional piece of information. Express your answer in slope- intercept form, if possible. (-2,-7)\(;\) parallel to the line \(\frac{1}{2} x-\frac{1}{3} y=5\)

a. Solve the equation \(x^{2}-2 x=b, b=8\) by first writing in standard form. Now plot both sides of the equation in the same viewing screen \(\left(y_{1}=x^{2}-2 x \text { and } y_{2}=b \right)\). At what. \(x\) -values do these two graphs intersect? Do those points agree with the solution set you found? b. Repeat (a) for \(b=-3,-1,0,\) and 5

Find an equation of a line that passes through the point \((-A, B-1)\) and is perpendicular to the line \(A x+B y=C\) Assume that \(A\) and \(B\) are both nonzero.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.