Interpret the expression in terms of Arctic Sea ice extent,...

Interpret the expression in terms of Arctic Sea ice extent, the area of sea covered by ice. $^{3}$ Let $E(x)$ and $F(t)$ be the Arctic Sea ice extent, both in millions of square kilometers, as a function of time, $x,$ in years, since February $1979,$ and time, $t,$ in days, since December $31,$ 2014 $$\frac{F(59)-F(32)}{59-32}=0.0159$$

Key Concepts

Units and Interpretation

When interpreting any rate of change, understanding the units is crucial. Here, the sea ice extent is given in millions of square kilometers and time is measured in days. Thus, the calculated rate of 0.0159 represents the average change in the sea ice extent (in millions of square kilometers) per day over the interval considered.

Average Rate of Change

This is a measure of how much a function's value changes on average for a unit change in its input. It is calculated as the difference in the function's values at two points divided by the difference in the corresponding input values. In this context, it quantifies how the Arctic Sea ice extent changes over a specified time period.

Transcript

00:01 So today we're going to be going over the derivative at a point, but more specifically, we're going to be going over how to interpret values and rates when it comes to real -life application questions.

00:16 Both values and rates are input and output functions, where values are usually in these sorts of questions, evaluate.

00:34 At a certain point in time where you usually get some sort of output, something that you're measuring, and rates are usually given within a certain time frame, like from one year to five years in the future, and you're trying to see the change per year or per whatever time you're giving of something that you're measuring.

01:01 In this question, we're given a rate of some kind.

01:07 And we're also given that f of t is a function that measures the sea ice, the art, yeah, the sea ice extent in millions of square kilometers.

01:25 And this t here is an input of time that is measured in days after december 31st of 2014.

01:43 So since we're given that, that makes understanding these a lot easier.

01:50 So we know that this one is after 59 days after december 31st, and this one is 32 days after december 31st.

02:00 So let's do this.

02:05 We know that january has 31 days.

02:12 February has 28 days.

02:17 So let's add those two numbers up to see if we get one of the numbers up.

02:21 We're given.

02:25 So 31 plus 28...