The table shows both the number of a certain type of graphing calculator in demand and the number supplied at certain prices.

Demand and Supply Schedules for a Graphing Calculator (Producers will supply no calculators when the market price is less than $47.50.)

Price (dollars per calculator)	Demand (million calculators)	Supply (million calculators)
60	35	10
90	31	32
120	15	50
150	5	80
180	4	100
210	3	120

(a) Find the function for the logistic model for demand in million calculators, where p is the price per calculator in dollars, with data from 60 p 210.(Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into your Y1.) D(p) = _________million calculators Find the function for linear model for supply in million calculators, where p is the price per calculator in dollars, with data from60 p 210. (Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into your Y2.)

p dollars per calculator, where 60 p 210. Tip: Be sure you are using the unrounded demand and supply functions for the calculations that follow. Using the rounded functions may result in incorrect answers. (b) At what price will market equilibrium occur? (Round your answer to two decimal places.) $_________ per calculator How many calculators will be supplied and demanded at this price? (Round your answer to two decimal places.) ____________million calculators (c) Calculate the producer surplus at market equilibrium. (Round your answer to three decimal places.) $________million Calculate the consumer surplus at market equilibrium. (Round your answer to three decimal places.) $________million Calculate the total social gain at market equilibrium. (Round your answer to three decimal places.) $________million

S(p)={forp