MrMcmath
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The half-life of a certain medicine is 30 hours. The equation below gives the amount of the medicine (g, in grams) remaining in the body after t hours since taking the medicine.
How many days after taking the medicine will there be 4 grams remaining in the body?

The halflife of a certain medicine is 30 hours The equation below gives the amount of the medicine g in grams remaining in the body after t hours since taking t class=

Respuesta :

chetankachana

Answer:

10 days

Step-by-step explanation:

Hello!

We basically have to plug in 4 for g and solve for the value of t.

Solve for T

  • [tex]g = 1024(\frac12)^{\frac{t}{30}}[/tex]
  • [tex]4 = 1024(\frac12)^{\frac{t}{30}}[/tex]
  • [tex]\frac{4}{1024} = (\frac12)^{\frac{t}{30}}[/tex]
  • [tex]\frac{1}{256} =( \frac12)^{\frac{t}{30}[/tex]

Using exponent rules, exponents with the same base have the same power. We can utilize this rule by converting 1/256 into an exponent with a base of 1/2.

  • [tex]\frac{1}{256} =( \frac12)^{\frac{t}{30}[/tex]
  • [tex](\frac12)^8 =( \frac12)^{\frac{t}{30}[/tex]
  • [tex]8 = \frac{t}{30}[/tex]
  • [tex]240 = t[/tex]

It will take 240 hours for there to be 4 grams remaining. To convert this into days, we have to divide by 24.

  • 240/24
  • 10

So it will take 10 days for 4 g to remain.

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