Question

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?

Answer 1

10 days

Explanation:

Hello!

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

Solve for T

• 
  `g = 1024(\frac12)^{(t)/(30)}`
• 
  `4 = 1024(\frac12)^{(t)/(30)}`
• 
  `(4)/(1024) = (\frac12)^{(t)/(30)}`
• 
  `(1)/(256) =( \frac12)^{(t)/(30)`

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.

• 
  `(1)/(256) =( \frac12)^{(t)/(30)`
• 
  `(\frac12)^8 =( \frac12)^{(t)/(30)`
• 
  `8 = (t)/(30)`
• 
  `240 = t`

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.