As blood moves away from the heart systolic pressure, in mm of mercury, after t seconds changes according to the function p(t) = 25t^2+125/t^2+1evaluate the instantaneous rate of change at t=5 seconds

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Supposing that the function is `p(t) = (25t^2+125)/(t^2+1), ` you need to differentiate the function p(t) with respect to t to evaluate the rate of change such that:

`p'(t) = ((25t^2+125)'*(t^2+1) - (25t^2+125)*(t^2+1)')/((t^2+1)^2)`

`p'(t) = (50t*(t^2+1) - 2t*(25t^2+125))/((t^2+1)^2)`

`p'(t) = (50t^3+ 50t- 50t^3 - 250t)/((t^2+1)^2)`

`p'(t) = (-200t)/((t^2+1)^2)`

You need to substitute 5 for t in p'(t) such that:

`p'(5) = (-200*5)/((26)^2)`

`p'(5) = (-50*5)/(13*13)`

`p'(5) = -250/169`

Hence, evaluating the rate of change yields of given function `p'(5) = -250/169.`