What are the importances of interpolation in the practical life?

Question

why we study interpolation? where is it needed in our daily life?

Answer 1

Interpolation is helpful whenever you have to scale things up or down.

Maybe you know how much catering costs for an event with 10 people and also 50 people as well as 100 people, but you need an accurate estimate of how much catering will cost for 25 people or 75.  That's a useful thing to know just for hosting a nice party.

Or maybe you are an entrepreneur with a small business that you are suddenly growing.  It's a professional thing to do, to predict what you will need as you scale up your business.  How many new employees?  How big a space?  Who is cleaning that space?  How much time will cleaning the space take?  How much time will it take to do work now that you have more employees?  How much will you theoretically be able to do in a day?  All of those could be answered with interpolation.

Maybe you are a server at a restaurant.  You should not only have a good idea of how much time it takes for the kitchen to make the food for your customers no matter how many of them there are.  You should also have a good idea of how long it takes a group to finish food so that you can go and check on them at an appropriate time.  That's interpolation.

Buying a car.  How much money will you put into a car that has a certain number of miles on it?  Will it be worth it?  Can you afford it?  That's interpolation.

How many gallons of gas will it take to get to a certain place?  How many times will you need to fill up?  What will that add to your travel time?  That's interpolation.

What are you interested in?  I can give you some more specific examples of how math relates to whatever field you are interested in.  I myself do math and theatre and there are a lot of times it is useful for me to have at least some basic math skills in the theatre.  Not when I'm acting, but when I help out in the scene shop.