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

Answer:

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

Step-by-step 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,

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