Production, Given the Amount Invested in Capital Capital, x (million dollars) Production, P (billion units) 6 20 18 39 24 41 зс 44 42 59 48 76 (a) Describe the behavior suggested by a scatter plot of the data and list the types of models that exhibit this behavior. A scatter plot of the data is increasing the right of x = 24. This behavior suggests a cubic to the left of x= 24 and concave up and appears to have an inflection point near x 24. The scatter plot is concave down to function. (b) Describe the possible end behavior as input increases and list the types of models that would fit each possibility. Production should continue to increase without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility Production should continue to increase to a limiting value as capital expenditure increases. A logistic model would fit this possibility. Production should decrease without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility Production should approach 0 as capital expenditure increases. A logistic model would fit this possibility. (c) Write the function of the model that best fits the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 48. (Round all numerical x values to four decimal places.) X million dollars (d) Write the function of the model that best exhibits the end behavior of the data of the production level in billion units, where invested in capital, with data from 6 xs 48. (Round all numerical values to four decimal places.)