A patient takes a medication with a half life. Initially, there are 11 milligrams of the medication in the patient's system. After 70 minutes there are 7 milligrams. After how many minutes will there be only 3 milligrams remaining in the patient’s system? here be after 10 hours? Round your answer to the nearest whole number, do not include units.

When the expression of function involves exponent. The time it will take so there be only 3 milligrams remaining in the patient’s system is 201 minutes.

What are exponential functions?

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called the exponential function.

The medicine was initially 11 milligrams, After 70 minutes there are 7 milligrams. Therefore, the rate at which the medicine will dilute in the body is,

[tex]F = Ie^{rt}\\\\7 = 11e^{(70 \times r)}\\\\r = \dfrac{\ln\frac{7}{11}}{70}\\\\r = -0.006457[/tex]

Now, the time it will take for the medicine to be only 3 milligrams is,

[tex]3 = 11e^{t \times -0.006457}\\\\\dfrac{\ln\frac{3}{11}}{ -0.006457} = t\\\\t = 201.22 \approx 201[/tex]

Hence, the time it will take so there be only 3 milligrams remaining in the patient’s system is 201 minutes.

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