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

Answer:[tex]y = 50(0.85)^{t}[/tex]Step-by-step explanation:Let the equation that models the decay of the substance is given by  [tex]y = y_{0} \times e^{-kt}[/tex] ........... (1) where y is the amount of the substance remaining after t hours and [tex]y_{0}[/tex] 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 [tex]0.5 = e^{- 4k}[/tex] Now, taking ln on both sides we get ln 0.5 = -4k ⇒ k = 0.17328 Therefore, the equation (1) becomes  [tex]y =50\times e^{-0.17328t}[/tex] {Since the initial amount of the substance was 50 gm} ⇒ [tex]y = 50(0.85)^{t}[/tex] (Approximate) (Answer)