Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Methane is a greenhouse gas implicated as a contributor to global warming. Given below is the table of values of [tex]Q = w(t)[/tex], the atmospheric methane level in parts per billion (ppb) [tex]t[/tex] years after 1980.

[tex]\[
\begin{array}{c|c|c|c|c|c|c|c}
\hline
t & 0 & 5 & 10 & 15 & 20 & 25 & 30 \\
\hline
Q & 1575 & 1660 & 1715 & 1750 & 1770 & 1775 & 1785 \\
\hline
\end{array}
\][/tex]

(a) Evaluate [tex]\frac{w(5) - w(0)}{5 - 0}[/tex] and [tex]\frac{w(15) - w(5)}{15 - 5}[/tex]. Round your answers to one decimal place.

[tex]\[
\begin{array}{l}
\frac{w(5) - w(0)}{5 - 0} = \frac{1660 - 1575}{5} = 17.0 \\
\frac{w(15) - w(5)}{15 - 5} = \frac{1750 - 1660}{10} = 9.0
\end{array}
\][/tex]

(b) Compare your answers in (a). What does this tell you about atmospheric methane levels? Enter a year in each box to complete the explanation.

This tells us that the methane level rises at a slower average rate from the years [tex] \square [/tex] to [tex] \square [/tex] than from the years [tex] \square [/tex] to [tex] \square [/tex].

[tex]\[
\begin{array}{l}
\text{This tells us that the methane level rises at a slower average rate from the years } \boxed{5} \text{ to } \boxed{15} \text{ than from the years } \boxed{0} \text{ to } \boxed{5}.
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Alright, let's go through the problem step-by-step:

#### (a) Evaluate [tex]\(\frac{w(5) - w(0)}{5 - 0}\)[/tex] and [tex]\(\frac{w(15) - w(5)}{15 - 5}\)[/tex]

We have the table of values:

[tex]\[ \begin{array}{c|c|c|c|c|c|c|c} \hline t & 0 & 5 & 10 & 15 & 20 & 25 & 30 \\ \hline Q & 1575 & 1660 & 1715 & 1750 & 1770 & 1775 & 1785 \\ \hline \end{array} \][/tex]

1. First, we calculate the average rate of change between [tex]\( t = 0 \)[/tex] and [tex]\( t = 5 \)[/tex]:

[tex]\[ \frac{w(5) - w(0)}{5 - 0} = \frac{1660 - 1575}{5 - 0} \][/tex]

[tex]\[ = \frac{85}{5} = 17.0 \][/tex]

2. Next, calculate the average rate of change between [tex]\( t = 5 \)[/tex] and [tex]\( t = 15 \)[/tex]:

[tex]\[ \frac{w(15) - w(5)}{15 - 5} = \frac{1750 - 1660}{15 - 5} \][/tex]

[tex]\[ = \frac{90}{10} = 9.0 \][/tex]

So, the average rates of change are:

[tex]\[ \frac{w(5) - w(0)}{5 - 0} = 17.0 \quad \text{ppb per year} \][/tex]

[tex]\[ \frac{w(15) - w(5)}{15 - 5} = 9.0 \quad \text{ppb per year} \][/tex]

#### (b) Compare your answers in (a). What does this tell you about atmospheric methane levels?

We notice that the rate of change [tex]\(\frac{w(5) - w(0)}{5 - 0}\)[/tex] is higher than the rate of change [tex]\(\frac{w(15) - w(5)}{15 - 5}\)[/tex].

This tells us that the methane level rises at a slower average rate from the years 5 to 15 than from the years 0 to 5.

To complete the explanation:

[tex]\[ \text{This tells us that the methane level rises at a slower average rate from the years} \, 0 \, \text{to} \, 5 \, \text{than from the years} \, 5 \, \text{to} \, 15. \][/tex]

So, the final answer is:

[tex]\[ \text{This tells us that the methane level rises at a slower average rate from the years} \, 0 \, \text{to} \, 5 \, \text{than from the years} \, 5 \, \text{to} \, 15. \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.