Sensor Error Effect on Integrated Volume
An ecologist observes water flow through a stream, modeling the cumulative volume as $$V(t)=\int_0^t 5*e^{0.3*x}\,dx$$. What would happen if the flow sensor error doubles the measured rate, changing the integrand to $$10*e^{0.3*x}$$; how does the total volume at time $$t$$ compare to the original?
A
The total volume doubles at any given time.
B
The total volume increases tenfold compared to the original.
C
The total volume increases by a constant amount over the original.
D
The flow rate doubles, but the total volume remains the same.
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