Some scientists say, happiness, when measured on a scale of 0 (super unhappy) to 100 (super happy), is a function of the number of hours you spend on instagram per day. They say when 0 hours spent, the average happiness level is 60, and each hour spent thereafter diminishes their happiness by 2. Express this statement in terms of a mathematical function

Question

Mathematics

Amira Pearson

3 July, 11:14

Some scientists say, happiness, when measured on a scale of 0 (super unhappy) to 100 (super happy), is a function of the number of hours you spend on instagram per day. They say when 0 hours spent, the average happiness level is 60, and each hour spent thereafter diminishes their happiness by 2. Express this statement in terms of a mathematical function

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Kelly Weeks · Answer 1

f (x) = 60-2x

Step-by-step explanation:

Suppose that f (x) = y is a happiness function. It is a function of the number of hours you spend on Instagram per day. That means that the output of the function will be a "happiness score", i. e. the value between 0 and 100, and the variable x will be an output value, the hours spent on Instagram daily.

We know that if we spend 0 hours on Instagram per day the happiness score will be 60, which means that:

f (0) = 60

If we spend 1 hour per day on Instagram our level of happiness will be decreased by 2, i. e. 60-2 = 58. Therefore,

f (1) = 58

If we spend 2 hours on Instagram per day our level of happiness will be decreased even more, i. e. 58-2 = 56. Therefore,

f (2) = 56

Notice that 56 = 60-4 = 60-2*2

If we spend 3 hours on Instagram per day our level of happiness will be decreased even more, i. e. 56-2 = 54. Therefore,

f (3) = 54

Notice that 54 = 60-6 = 60-3*2

Now we can see the pattern from which the level of happiness can be calculated. It is 60 decreased by the number of hours multiplied by 2.

Hence, the "happiness function" is:

f (x) = 60-x*2 = 60-2x, where x is a number of hours spent on Instagram.