Derivative as an Instantaneous Rate of Change
A population is modeled by the function , where $t$ is time in years. The derivative of the function is . If $P'(t)$ is interpreted as the exact number of individuals added to the population per year, what is the primary conceptual error in this interpretation?
A
They incorrectly differentiated the exponential function.
B
They should have used the natural logarithm to compute the derivative.
C
They misunderstood that the derivative represents an instantaneous rate of change, not a discrete count per year.
D
They omitted the effect of the constant 100 in the interpretation of the rate.
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