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Mekhanik [1.2K]
3 years ago
9

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.
Biology
1 answer:
Nimfa-mama [501]3 years ago
3 0

Answer:

-1.1

Explanation:

Data provided in the question:

Average temperature is rising at a rate, \frac{dT}{dt} = 0.15°C/year

Rate of change  rainfall, \frac{dR}{dt} = - 0.1 cm/year

\frac{\delta W}{\delta T} = -2

\frac{\delta W}{\delta R} = 8

Now,

we need to calculate \frac{dW}{dt}

since,

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

thus, Using the chain rule , we have

\frac{dW}{dt} = \frac{\delta W}{dT}\times\frac{dT}{dt} +  \frac{\delta W}{dR}\times\frac{dR}{dt}

on substituting the respective values, we get

\frac{dW}{dt} = -2 × 0.15 +  8 × (-0.1)

or

\frac{dW}{dt} = -0.3 - 0.8

or

\frac{dW}{dt} = -1.1

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