Sensor Error Effect on Integrated Volume

Question

An ecologist models the cumulative volume of water flowing through a stream with the function $$V(t)=\int_0^t 5*e^{0.3*x}\,dx$$. Suppose a sensor error doubles the measured flow rate, which changes the integrand to $$10*e^{0.3*x}$$. How does the new cumulative volume at time $$t$$ compare to the original cumulative volume?

Accepted Answer

The total volume doubles at any given time.

Answer

The flow rate doubles, but the total volume remains the same.

Answer

The total volume increases by a constant amount over the original.

Answer

The total volume increases tenfold compared to the original.

Sensor Error Effect on Integrated Volume

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