Alina is an ecologist who studies the change in the bear population of Siberia over time. The relationship between the elapsed time, t, in years, since Alina began studying the population, and the total number of bears, N(t), is modeled by the following function

N(t)=2187⋅(0.67)t

In the xy-plane, if the parabola with equation passes through the point (-1, -1), which of the following must be true?

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

Astudent has created the give circuit diagram. it consists of a battery, a resistor, and a light bulb. in one minute, 1.2c of charge flows through the resistor. how much charge flows through the light bulb in one minute?