What kind of function best models each situation? write linear, quadratic, exponential, trigonometric, or piecewise.

1. a radioactive element has a half-life of 20 minutes. a sample contains 66 g of the element. a function models the amount of the sample remaining as a function of time.

2. a function models the nth term in the following sequence: 8.5, 5, 1.5, -2, -5.5,

and you. much appreciated.

1.two more than the quotient of a number and 6 is equal to 7 use the c for the unknown number translate the sentence into an equation

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.

Parabolas y=−2x^2 and y=2x^2+k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.