Mathematics

The manager of a store recorded the annual sales S (in thousands of dollars) of a product over a period of 7 years, as shown in the table, where t is the time in years, with t = 6 corresponding to 2006. t s 6 5.4 7 6.9 8 11.5 9 15.5 10 19.0 11 22.0 12 23.6 a. Use the regression features of a graphing calculator to find a model of the form S = a + bť + ct+d for the data above. (2 points) b. Use a graphing calculator to plot the data and sketch the model. (2 points) c. Use calculus and the model to find the time t when sales were increasing at the greatest rate. (4 points) d. Do you think the model would be accurate for predicting future sales? Explain. (2 points)

EXPERT ANSWER a) Putting the values in desmos, we get the estimated model to be the following: b) The graph of the data is the following: c) Observe that when the sales was increasing as greatest rate, then Hence the sales at that time would be d) No, the model would not be great for …

The manager of a store recorded the annual sales S (in thousands of dollars) of a product over a period of 7 years, as shown in the table, where t is the time in years, with t = 6 corresponding to 2006. t s 6 5.4 7 6.9 8 11.5 9 15.5 10 19.0 11 22.0 12 23.6 a. Use the regression features of a graphing calculator to find a model of the form S = a + bť + ct+d for the data above. (2 points) b. Use a graphing calculator to plot the data and sketch the model. (2 points) c. Use calculus and the model to find the time t when sales were increasing at the greatest rate. (4 points) d. Do you think the model would be accurate for predicting future sales? Explain. (2 points) Read More »

Problem 2: f(x) = x + e

x 2 1) Find the equation of the tangent line to f at the point (0;1) 2) Use the tangent line at the point (0;1) to approximate the value of f(0:1). 3) Is the approximation found previously an over or under estimate of the actual value of f(0:1)? Justify your answer EXPERT ANSWER

5. The figure shows the graphs of the position, velocity, and acceleration of a car. Identify each curve and justify your answers. (12 points) 6. Given the function f(x) = x + 4x a. Find the relative extrema of f. (4 points) i no elsvietni lis bns biswa svono a todas as now no sleva (etnog) niebeb vnosa b. Find the tangent line approximation of fat x = -1.(4 points) nog dobitni lotnico C. Use your tangent line approximation to approximate the value of f(-1.01). d. Is your approximation an underestimate or overestimate of the actual value of f-1.01)? Justify your answer. (1 point)

EXPERT ANSWER