Question

The half life of a certain substance is about 4 hours. The graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours.
A graph shows time (hours) labeled 1 to 10 on the horizontal axis and quantity (grams) on the vertical axis. A line decreases from 0 to 9.

Which function can be used to determine the approximate number of grams of the sample remaining after t hours?

y = 25(0.15)t
y = 25(0.85)t
y = 50(0.15)t
y = 50(0.85)t

Answer 1

Answer:

D

Step-by-step explanation:

50(.85)^t

Answer 2

Answer:

$y = 50(0.85)^{t}$

Step-by-step explanation:

Let the equation that models the decay of the substance is given by  

$y = y_{0} \times e^{-kt}$ ........... (1)

where y is the amount of the substance remaining after t hours and $y_{0}$ represents the initial amount of the substance and k is the decay rate constant.

Now, given that the half-life period of the substance is 4 hours.

So, from equation (1) we can write

$0.5 = e^{- 4k}$

Now, taking ln on both sides we get

ln 0.5 = -4k

⇒ k = 0.17328

Therefore, the equation (1) becomes  

$y =50\times e^{-0.17328t}$ {Since the initial amount of the substance was 50 gm}

⇒ $y = 50(0.85)^{t}$ (Approximate) (Answer)