Question

The amount of radioactive uranium changes with time. The table below shows the amount of radioactive uranium f(t) left after time t:

t(hours) 0 0.5 1
f(t) 100 50 25

Which exponential function best represents the relationship between f(t) and t?

A).f(t) = 100(0.25)t

B).f(t) = 0.25(100)t

C).f(t) = 100 (0.5)t

D).f(t) = 0.25(50)t

Answer 1

A).f(t) = 100(0.25)t

because 100 is our y-intercept since it's 100 when t equals 0. After 1 day, f(t) = 25 because when we plug in 1 in our equation,
f(t) = 100(0.25)^1
f(t) = 100(0.25)
f(t) = 25

Answer 2

`f(t) = 100(0.25)^t`

Explanation:

The general exponential function is,

`f(t)=ab^t`

The points given in the table are,

`(0,100),(0.5,50),(1,25)`

Putting
`(0,100),(1,25)` in the general equation, we get

`\Rightarrow 100=ab^0`

`\Rightarrow a=100`

And

`\Rightarrow 25=ab^(1)`

`\Rightarrow ab=25`

Putting the value of a,

`\Rightarrow 100b=25`

`\Rightarrow b=0.25`

Now the exponential function becomes,

`f(t) = 100(0.25)^t`