Answer:
-1.1
Explanation:
Data provided in the question:
Average temperature is rising at a rate, [tex]\frac{dT}{dt}[/tex] = 0.15°C/year
Rate of change rainfall, [tex]\frac{dR}{dt}[/tex] = - 0.1 cm/year
[tex]\frac{\delta W}{\delta T}[/tex] = -2
[tex]\frac{\delta W}{\delta R}[/tex] = 8
Now,
we need to calculate [tex]\frac{dW}{dt}[/tex]
since,
The wheat production (W) is dependent on the rainfall (R) and the Temperature (T)
thus, Using the chain rule , we have
[tex]\frac{dW}{dt}[/tex] = [tex]\frac{\delta W}{dT}\times\frac{dT}{dt}[/tex] + [tex]\frac{\delta W}{dR}\times\frac{dR}{dt}[/tex]
on substituting the respective values, we get
[tex]\frac{dW}{dt}[/tex] = -2 × 0.15 + 8 × (-0.1)
or
[tex]\frac{dW}{dt}[/tex] = -0.3 - 0.8
or
[tex]\frac{dW}{dt}[/tex] = -1.1
