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Answer:
The rate of change of blood pressure at the 50-pound weight level is 0.26
The rate of change of blood pressure at the 80-pound weight level is 0.16
Step-by-step explanation:
We have, P(x) = 12.9(9 + ln x)
We need to compute the rate of change of blood pressure P(x) so, we will differentiate the function P(x) with respect to x.
P(x) = 12.9(9 + ln x)
P(x) = 116.1 + 12.9ln x
Differentiating with repect to x:
= 0 + 12.9 (
)
= 12.9 (
)
The differential of ln x is and the differential of constant terms is 0.
The rate of change of blood pressure at the 50-pound weight level can be calculate by substituting 50 in place of x, so
= 12.9 (
)
= 12.9 * (1/50)
= 0.258
= 0.26
Similarly, The rate of change of blood pressure at the 80-pound weight level can be calculate by substituting 80 in place of x, so
= 12.9 (
)
= 12.9 * (1/80)
= 0.16125
= 0.16