Which graph represents an exponential growth function?
1 answer:
You might be interested in
Answer:
416 in²
Step-by-step explanation:
Given that:
Height. h = 4 in
Length = 12 in
Width = 10 in
The surface area of a rectangular prism is obtained using the relation :
Surface Area, S = 2(lw + lh + wh)
S = 2[(10*12) + (10*4) + (12*4))
S = 2(120 + 40 + 48)
S = 2(208)
S = 416 in²
Answer:
- h ≥ 0
- C = 0; concentration eventually decays to nothing
- (0, 0) is the only intercept in the domain. It means the concentration in the bloodstream is zero at the time the drug is injected.
- 1.95 hours
Step-by-step explanation:
1. a. The domain of the function in the context of this problem is h ≥ 0. The maximum value of h will correspond to the time at which the concentration is considered to be negligible. If that time is when the concentration decays to 1% of its peak value, then perhaps the suitable domain is 0 ≤ h ≤ 180.
b. The equation of the vertical asymptote of this function is where the denominator of C(h) is zero, that is ...
h^3 +8 = 0
h = ∛(-8)
h = -2 . . . . the equation of the vertical asymptote
This is not a concern for a medical professional because it is outside the domain of the function.
__
2. As h gets large the value of the function approaches 2/h, which is to say the horizontal asymptote is C = 0. It means the concentration of medication in the blood eventually decays to zero.
__
3. C(0) = 0 is the only intercept in the domain of the function. (h, C(h)) = (0, 0)
In the context of this problem, it means the blood concentration of medication is zero at the time of the injection.
__
4. About 1.95 hours after injection, a maximum concentration of the drug occur in the bloodstream. This value is easily found using a graphing calculator.
Taking the derivative of the function gives you ...
C'(h) = -2(h^4 +5h^3 -16h -20)/(h^3 +8)^2
This has two real zeros and two complex zeros. The positive real zero is near h = 1.94527, about 1.95.
That is, the concentration in the bloodstream reaches a maximum about 1.95 hours after injection into the muscle.
