A radioactive substance has a half-life of 7 hours. If a sample of the substance has an initial mass of 2000g, estimate the instantaneous rate of change in mass 1.5 days later a. -5.6 g/h
b. -56 g/h
c. -707 g/h
d. -0.845 g/h

9514 1404 393

  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.

__

Many graphing calculators have derivative functions that can find this for you.

step-by-step explanation:

wrgasadvauoyfaiua-00uhf