A The function Would this concern a medical professional Ex

A.) The function

} Would this concern a medical professional? Explain.

B.) Using the function from question number 11, find the equation of the horizontal asymptote. What does this mean in this context?

C.) Using the function from question number 11, find the equation of the horizontal asymptote. What does this mean in this context?

D.) Using the function from question 11, how many hours after injection does a maximum concentration of the drug occur in the bloodstream? Round answer to nearest hundredth.

E.) Suppose you need to re-administer this injection at the point when the concentration is less than 0.5%. If the first injection was given at 8:00 am, what time should the next injection be given? Use the function from question number 11.

Solution

(2h^2 + 5h) / (h^3 + 8)

VA :
h^3 + 8 = 0
h^3 = -8
h = -2

So, VA is : h = -2

This\'d not concern anyone cuz h for hrs
cannot be negative

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B)
Numerator degree = 2
Den degree = 3

So, since deg of num < deg of den,
HA : y = 0

This means, with h ----> inf,
the concentration of medication approaches0

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C)
Same as B

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D)
f = (2h^2 + 5h) / (h^3 + 8)

Deriving by quotient rule :
u = 2h^2 + 5h         v = h^3 + 8
u\' = 4h + 5          v\' = 3h^2

(u\'v - uv\') / v^2

((4h+5)(h^3+8) - (3h^2)(2h^2 + 5h)) / (h^3 + 8)^2 = 0

(4h^4 + 5h^3 + 32h + 40 - 6h^4 - 15h^3) / (h^3 + 8)^2 = 0

So, crossmultiplying :
-2h^4 - 10h^3 + 32h + 40 = 0

Divide -2 all over :
h^4 + 5h^3 - 16h - 20 = 0

h = 1.9453

So, approx h =1.95

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e)
(2h^2 + 5h) / (h^3 + 8) < 0.5

Cross multiply :
2h^2 + 5h < 0.5h^3 + 4

Multiply by 2 :
4h^2 + 10h < h^3 + 8

h^3 - 4h^2 - 10h + 8 > 0

We get h > 5.544 here

8 am is h = 0
So, h = 5.544 is approx 1:30 pm ---> ANS