Hi, can I have some help with these math questions, please?

The number, N, of people who have heard a rumor spread by mass media at time, t, is given by N(t) = a(1 - e-kt) There are 131000 people in the population who hear the rumor eventually. 5 percent of them heard it on the first day. Find a and k, assuming t is measured in days. a k =Find a and b such that a curve of the form y = e (T-a) / for b > 0 has a local maximum at x = 5 and points of inflection at x = -9 and x = 19. Select a blank to input an answer SAVE ? HELP REP Consider f(a) = a(1 - e-br) for a > 0 and b > 0. Then, h (1) f'(x) = and f(x) is (2) f"(z) = and f(x) is Select a blank to input an answer SAVE ? HELP ORMAX-MIN Problem Let f(x) = etz - kx, for k > 0. Using a calculator or computer, sketch the graph of f for k = 1 1 1 1 9 ' 6' 3' 2, 1, 2, 4. Describe what happens as k changes. (1) f(x) has a local minimum. Find the location of the minimum: a (2) Find the y-coordinate of the minimum: y = (3) Find the value of k for which this y-coordinate is largest: k (4) How do you know that this value of k maximizes the y-coordinate? Find - 172 to use the second derivative test: 12 dry Important: Note that the derivative you get is negative for all positive values of k, and make sure you understand that this means that your value of k maximizes the y-coordinate of the minimum.)The power, P, dissipated when a 3-volt battery is put across a resistance of R ohms is given by P = 9 R What is the rate of change of power with respect to resistance? rate of change = V /ohm? Select a blank to input an answer SAVE For positive constants k and g, the velocity, v, of a particle of mass m at time t is given by mg K (1 e kt /m (1) At what rate is the velocity is changing at time t # 0? rate (2) At what rate is the velocity is changing at time t - 10? rate (What do your answers tell you about the motion of the particle?)A voltage V across a resistance R generates a current I = V/ R. If a constant voltage of 12 volts is put across a resistance that is increasing at a rate of 0.3 ohms per second when the resistance is 19 ohms, at what rate is the current changing? rate amp / sCoroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air temperature of 70 degrees F and a living body temperature of 98.6 degrees F, the temperature T(t) in degrees F of a body at a time t hours since death is given by T(t) - 70 + 28.6e kt (1) For what value of k will the body cool by 2 degrees F in the first hour? k (2) Using the value of k found above, after how many hours will the temperature of the body be decreasing at a rate of 1 degree F per hour? after hours (3) Using the value of k found above, show by calculating both values that, 24 hours after death, the coroner's rule of thumb gives approximately the same temperature as the formula. T(24) Rule of thumb gives T = OFFor the figures below, determine the nature of lim , if f(x) is shown as the blue curve and g() as the black curve. 8(x) f ( x) What can we tell about lim f(2) ? I-+a g(I) O Limit exists and is zero Limit doesn't exist Limit exists and is negative We don't have enough information to decide whether the limit exists or not Limit exists and is positiveor the figures below, determine the nature of lim , if f(x) is shown as the blue curve and g(x) as the black curve. g(x) f (x) What can we tell about lim J(2) ? x -a g(z) X Limit exists and is positive Limit exists and is zero Limit exists and is negative We don't have enough information to decide whether the limit exists or not Limit doesn't exist