9514 1404 393
Answer:
a. -5.6 g/h
Step-by-step explanation:
The mass of the substance can be described by the equation ...
m(t) = 2000(1/2)^(t/7)
where t is in hours and m(t) is in grams.
Then the rate of change is found by differentiating the function:
m'(t) = 2000(1/2)^(t/7)·(1/7)·ln(1/2)
1.5 days is 36 hours, so we want ...
m'(36) = (2000/7)ln(1/2)(1/2)^(36/7) ≈ (-198.04)(0.0283) ≈ -5.605
The rate of change of mass after 1.5 days is -5.6 grams per hour.
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Many graphing calculators have derivative functions that can find this for you.
