Wheat production w in a given year 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°c/year and rainfall is decreasing at a rate of 0.1 cm/year. they also estimate that, at current production levels, δw/δt = -2 and δw/δr = 8. estimate the current rate of change of wheat production, dw/dt.

-1.1

Explanation:

Data provided in the question:

Average temperature is rising at a rate, = 0.15°C/year

Rate of change  rainfall, = - 0.1 cm/year

= -2

= 8

Now,

we need to calculate

since,

The wheat production (W) is dependent on the rainfall (R) and the Temperature (T)

thus, Using the chain rule , we have

= +  

on substituting the respective values, we get

= -2 × 0.15 +  8 × (-0.1)

or

= -0.3 - 0.8

or

= -1.1

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