APFIVE Derivative as an Instantaneous Rate of Change
In a study of population growth, a student differentiates the function
$$ P(t) = 100 * e^{0.05 * t} $$
and obtains
$$ P'(t) = 5 * e^{0.05 * t} $$
then interprets this derivative as the exact number of individuals added per year. What conceptual mistake did they make?
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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