A block of ice weighing 100 kilograms begins to melt. Each hour the block loses 5%, of its weight. Let's let W be the weight in kilograms of the block of ice after melting for t hours.
Is W a linear function or an exponential function?
This function is exponential because W decreases by 9.75, as t increases from t=0 to t=2 .
This function is linear because W decreases by 5 as t increases from t=0 to t=1.
This function is linear because W is multiplied by a factor of 5% each time t increases by 1.
This function is exponential because W is multiplied by a factor of 0.95 each time t
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The question is asking you to evaluate if the rate of change is in fixed proportion to the amount or just in a fixed proportion to x.
If linear then you wont get a rate of change % in relation to the current amount, but you will see a fixed change for each step of x.
If exponential you wont see any change in the rate of change relative to the amount it will stay at a fixed % for each step of x
so the thing to ask is.. "is the % of change fixed or changing for each step of x"?
If fixed then exponential.. f[x+1]/f[x] is going to be constant.
Or "is the function just changing by the same amount for each step of x " so f[x+1]-f[x] is going to be constant. Then the function is linear.