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4. (4 points) Alfador produces gear for a racquetball league. It costs him $0.005 per square centimeter to produceracquetballs for the league. In the past, the league used racquetballs with diameter 4 cm, and he produced 30,000racquetballs. However, league regulations now require racquetballs to have diameter 4.05 cm.Use differentials to estimate the increase in cost that Alfador must suffer in order to produce 30,000 racquetballsunder its new regulations. Should this be an overestimate or an underestimate?You may use the fact that the surface area of a ball satisfiesS=πX2, wereXis the diameter of the ball.5. (5 points overall) In this problem, we will use linearization to approximate the solution ofet=t10+ 1.1 whichoccurs near the origin.(a) (2 pts) Without using a calculator, show that the equationet=t10+1.1 must have a solution in the interval[0,1]. You must fully justify your answer to receive full credit.(b) (3 pts) Replaceetby its linearization ata= 0 in the equation in part (a). Solve the new equation to get anapproximate solution to the original equation.Solution:6. (2 pts) A study of Norway’s railways revealed that, for rides up to 60 km, the price elasticity of the volume ofpassenger demand was approximately-0.4. Estimate the percent change in demand when the fare is increasedby 10%.