Question

GIVING BRAINLIEST A medical team has found that the blood concentration of a particular medicine has a decay rate of 40% in 24 hours. How much of an initial dose of 1,000 mg of the medicine will be detected after 48 hours? Round to the nearest mg
920 mg

200 mg

449 mg

360 mg

600 mg

Answer 1

Answer:

360 mg.

Step-by-step explanation:

The medicine has a decay rate of 40% in 25 hours, which means after 24 hours its amount will be 100% - 40% = 60% it's original value.

Let us call $t$ the number of hours passed and $d$ the number of 24-hours passed, then we know that

$t = 24d$.

Now, the amount $c$ of medicine left after time $d$ (dth 24-hour) will be

$c = 1000(0.6)^d$

and since $t =24d$, we have

$\boxed{c = 1000(0.6)^{\frac{t}{24} }}$

We now use this equation to find the final amount after $t =48 hours$:

$c = 1000(0.6)^{\frac{48}{24} }$

$c = 1000(0.6)^2 }$

$\boxed{c =360mg}$