The table lists the time, t, in seconds that an average athlete takes to swim 100 meters freestyle at age x years. Time That an Average Athlete Takes to Swim 100 Meters Freestyle Age Time Age Time (years) (seconds) (years) (seconds) 8 92 22 50 10 84 24 49 12 70 26 51 14 60 28 53 16 58 30 57 18 54 32 60 20 51 (a) Find a function for the model of the data that gives the time required for an average athlete to swim 100 meters freestyle at an age of x years, with data from 8 s x's 32. (Round all numerical values to three decimal places.) t(x) = (b) Calculate the age at which the minimum swim time occurs. (Round your answer to three decimal places.) yr Calculate the minimum swim time. (Round your answer to one decimal place.) sec (c) According to the table, at what age does minimum swim time occur? yr According to the table, what is the minimum swim time? sec 11. [-/10 Points] DETAILS LCALCCON5 4.1.005. MY NOTES ASK YOUR TEACHER Consider the following function. ((3) = 15, f'(3) = 3.2; x = 3.5 (a) Write a linearization for f with respect to x. FL(x ) = (b) Use the linearization to estimate fat the given input. f_(3.5) =