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.

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

a
y = 50(0.85)x

b
y = 25(0.15)x

c
y = 50(0.15)x

d
y = 25(0.85)x

Answer 1

Okay, so a half-life means that every so and so (which in this case is 4 hours), what we have is now equal to half of that (although it does do this more gradually).

The answer to this would be 50(0.85)x

Answer 2

Option A -
`y=50(0.85)^x`

Explanation:

Given : 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.

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

Solution :

The general form of exponential is
`y=ab^x`

where a is the initial value , b is the growth or decay rate.

We have given initial value is 50 i.e, a=50

The half life of a certain substance is about 4 hours.

x=4 ,
`y=(50)/(2)=25`

Substitute in the general form,

`y=ab^x`

`25=50(b^4)`

`b=((1)/(2))^{(1)/(4)}`

`b=0.85`

Therefore, The exponential function form is
`y=50(0.85)^x`

Hence, Option A is correct.