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Chapter 1: Problem 7

Let \(W=f(t)\) represent wheat production in Argentina, \(^{3}\) in millions of metric tons, where \(t\) is years since 2006 Interpret the statement \(f(4)=14\) in terms of wheat production.

Short Answer

Expert verified
In 2010, Argentina's wheat production was 14 million metric tons.

Step by step solution

01

Understanding the Notation

The notation given is \( f(4) = 14 \). Here, \( f \) represents the function that gives wheat production in millions of metric tons, and \( t \) represents years since 2006.
02

Determine the Year

Since \( t = 4 \), we calculate the year by adding 4 to 2006 because we are measuring time in years since 2006. This means \( t = 4 \) corresponds to the year 2010.
03

Interpret the Function Value

The function value \( f(4) = 14 \) indicates the production amount. Therefore, in the year 2010, the wheat production was 14 million metric tons.
04

Combine the Information

Putting it all together, the statement \( f(4) = 14 \) means that in the year 2010, which is 4 years after 2006, wheat production in Argentina was 14 million metric tons.

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Key Concepts

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

Wheat Production
Wheat production refers to the process and amount of growing and harvesting wheat, a staple crop with global significance. In agricultural terms, "wheat production" often highlights the total yield a country achieves within a specific time frame.
In Argentina's case, wheat production is crucial for its economy as wheat is a major export commodity.
  • Wheat is grown primarily in the Pampas region, where the climate and soil are well-suited for its cultivation.
  • The production process involves sowing, growing, and harvesting, which are affected by factors like agricultural techniques, climate conditions, and government policies.
By examining wheat production figures, we can assess the agricultural output strength and its impact on food supply and trade. Understanding wheat production is key in analyzing how countries like Argentina contribute to the global grain supply.
Time Since 2006
The notion of "time since 2006" serves an important role in describing dynamics over a set period. Here, it is a way to simplify the expression of years by using 2006 as a reference point. This approach allows functions like \( f(t) \) to efficiently map data points over time.
  • By setting 2006 as the baseline year, calculations become straightforward as years are expressed as an offset from 2006.
  • In our exercise, \( t \) is the variable representing the number of years since 2006, helping us focus on the trend of data over time without confusion over calendar years.
This concept is often used in mathematics and data analytics for clarity and simplification when interpreting timelines.
Metric Tons
Metric tons (or tonnes) are the units used to quantify wheat production in the given function. A metric ton is equal to 1,000 kilograms or approximately 2,204.62 pounds. This standardized measurement is essential for comprehending and comparing agricultural data globally.
  • Using metric tons allows consistent reporting of production volumes across countries, ensuring data is comparable regardless of local measurement systems.
  • In the context of wheat production, larger quantities like millions of metric tons are often used to reflect the scale of agricultural yields accurately.
Understanding metric ton measurements offers insights into the magnitude of production and facilitates international trade and policy decisions.
Argentina
Argentina is a key player in the global agricultural market, known for its vast fertile plains, which are ideal for wheat cultivation. The country is among the top wheat producers worldwide, contributing significantly to its economy and the global food supply.
In the context of this exercise, Argentina represents both the location and scale of wheat production.
  • Its agricultural sector benefits from favorable climatic conditions and advanced farming techniques.
  • Argentina's wheat production is crucial not just for local consumption, but as an essential export commodity.
By analyzing Argentina's wheat production data, one can glean insights into both historical trends and potential future developments in its agricultural capabilities.

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Most popular questions from this chapter

Table 1.43 gives values for \(g(t),\) a periodic function. (a) Estimate the period and amplitude for this function. (b) Estimate \(g(34)\) and \(g(60)\). Table 1.43 $$\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\\\\hline g(t) & 14 & 19 & 17 & 15 & 13 & 11 & 14 & 19 \\\\\hline t & 16 & 18 & 20 & 22 & 24 & 26 & 28 & \\\\\hline g(t) & 17 & 15 & 13 & 11 & 14 & 19 & 17 \\\\\hline\end{array}$$

Allometry is the study of the relative size of different parts of a body as a consequence of growth. In this problem, you will check the accuracy of an allometric equation: the weight of a fish is proportional to the cube of its length. \(^{87}\) Table 1.40 relates the weight, \(y,\) in \(\mathrm{gm}\), of plaice (a type of fish) to its length, \(x,\) in \(\mathrm{cm} .\) Does this data support the hypothesis that (approximately) \(y=k x^{3} ?\) If so, estimate the constant of proportionality, \(k\) $$\begin{array}{r|r|r|r|r|r} \hline x & y & x & y & x & y \\ \hline 33.5 & 332 & 37.5 & 455 & 41.5 & 623 \\ 34.5 & 363 & 38.5 & 500 & 42.5 & 674 \\ 35.5 & 391 & 39.5 & 538 & 43.5 & 724 \\ 36.5 & 419 & 40.5 & 574 & & \\ \hline \end{array}$$

In 2010 , there were about 246 million vehicles (cars and trucks) and about 308.7 million people in the US. \(^{70}\) The number of vehicles grew \(15.5 \%\) over the previous decade, while the population has been growing at \(9.7 \%\) per decade. If the growth rates remain constant, when will there be, on average, one vehicle per person?

A person breathes in and out every three seconds. The volume of air in the person's lungs varies between a minimum of 2 liters and a maximum of 4 liters. Which of the following is the best formula for the volume of air in the person's lungs as a function of time? (a) \(y=2+2 \sin \left(\frac{\pi}{3} t\right) \quad\) (b) \(\quad y=3+\sin \left(\frac{2 \pi}{3} t\right)\) (c) \(y=2+2 \sin \left(\frac{2 \pi}{3} t\right)\) (d) \(y=3+\sin \left(\frac{\pi}{3} t\right)\)

The population of a city is 50,000 in 2008 and is growing at a continuous yearly rate of \(4.5 \%\) (a) Give the population of the city as a function of the number of years since \(2008 .\) Sketch a graph of the population against time. (b) What will be the city's population in the year \(2018 ?\) (c) Calculate the time for the population of the city to reach \(100,000 .\) This is called the doubling time of the population.
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