# What is the significance of the partials in wheat production changes?

• skipo
In summary, wheat production in a given year is affected by the average temperature and annual rainfall, with a current rate of change of 0.15 degrees celsius per year and 0.1 cm per year respectively. Scientists estimate that at current production levels, an increase in temperature will lead to a decrease in wheat production (∂W/∂T = -2), while a decrease in rainfall will lead to an increase in wheat production (∂W/∂R = 8). The signs of the partial derivatives indicate the direction of change in wheat production with respect to each variable. To estimate the current rate of change of wheat production (dW/dt), the multivariable chain rule must be used, taking into account
skipo
1. Homework Statement
Wheat production in a given year, W, depends on the average temperature T and the annual rainfall R. Scientists estimate that the average temperature is rising at a rate of 0.15 degrees celsius per year and rainfall is decreasing at a rate of 0.1 cm per year. The also estimate that, at current production levels, ∂W/∂T = -2 and ∂W/∂R = 8.

a) what is the significance of the signs of the partials?
b) estimate the current rate of change of wheat production dW/dt.

Firstly, what is your attempt at this question? To start you off, for a), note that a partial derivative of a multi-variable function with respect to a paricular variable tells you the increase or decrease (depending on whether it is positive or negative)of the function with respect to that variable alone.

For b), you have to use the multivariable chain rule here. dW/dt can be expressed in terms of partial derivatives of T and R, along with the derivatives of T and R with respect to t.

## 1. What is the purpose of "Average temperature homework"?

The purpose of "Average temperature homework" is to calculate the average temperature of a given location over a specific period of time. This can help track weather patterns and climate changes.

## 2. How is the average temperature calculated?

The average temperature is calculated by adding the temperatures recorded at different intervals and then dividing the sum by the number of intervals.

## 3. What units are used for average temperature?

The units used for average temperature can vary, but the most commonly used units are degrees Celsius (°C) or degrees Fahrenheit (°F).

## 4. What factors can affect the accuracy of average temperature calculations?

Some factors that can affect the accuracy of average temperature calculations include the location of temperature readings, time intervals between readings, and any extreme or unusual temperature fluctuations.

## 5. What is the significance of knowing the average temperature?

Knowing the average temperature can provide important information for various fields such as agriculture, meteorology, and climatology. It can also help with predicting future weather patterns and understanding the impact of climate change.

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