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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

Respuesta :

alexab1023
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

InesWalston

Answer:

[tex]f(t) = 100(0.25)^t[/tex]

Step-by-step explanation:

The general exponential function is,

[tex]f(t)=ab^t[/tex]

The points given in the table are,

[tex](0,100),(0.5,50),(1,25)[/tex]

Putting [tex](0,100),(1,25)[/tex] in the general equation, we get

[tex]\Rightarrow 100=ab^0[/tex]

[tex]\Rightarrow a=100[/tex]

And

[tex]\Rightarrow 25=ab^{1}[/tex]

[tex]\Rightarrow ab=25[/tex]

Putting the value of a,

[tex]\Rightarrow 100b=25[/tex]

[tex]\Rightarrow b=0.25[/tex]

Now the exponential function becomes,

[tex]f(t) = 100(0.25)^t[/tex]


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