Question
Researchers have found that the risk of coronary heart disease rises as blood cholesterol increases. This risk may be approximated by the function
,
, where
is the risk in terms of coronary heart disease incidence per 1000 per year, and c is the cholesterol in
. Suppose a person’s cholesterol is 176
and going up at a rate of
per year. At what rate is the person’s risk of coronary heart disease going up?
The person’s risk of coronary heart disease is going up at the rate of
coronary heart disease incidence per 1000 per year per mg/dL of cholesterol.
(Round to three decimal places as needed.)
The person’s risk of coronary heart disease is going up at the rate of
(Round to three decimal places as needed.)
Ask by Lambert Campos. in the United States
Feb 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The person’s risk of coronary heart disease is increasing at a rate of 0.811 incidence per 1000 per year.
Solution

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Bonus Knowledge
To find the rate at which the person’s risk of coronary heart disease is increasing, we need to differentiate the function
with respect to
.
First, let’s find
:
Next, we plug in
:
Calculate
:
Now compute
:
Now substitute these values into
:
Now we find out how fast the risk is increasing with respect to cholesterol, given that cholesterol is increasing at
:
Therefore, rounding to three decimal places, the person’s risk of coronary heart disease is going up at the rate of approximately 0.718 coronary heart disease incidences per 1000 per year per mg/dL of cholesterol.