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The amount of a radioactive material changes with time. The table below shows the amount of radioactive material f(t) left after time t: t(hours) 0 1 2 f(t) 180 90 45 Which exponential function best represents the relationship between f(t) and t? f(t) = 0.5(180)t f(t) = 180(0.25)t f(t) = 180(0.5)t f(t) = 0.5(50)t

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JeanaShupp

Answer:- The exponential function best represents the relationship between f(t) and t is [tex]f(t)=180(0.5)^t[/tex]

Explanation:-

The exponential function is given by [tex]f(t)=Ab^t[/tex] , where A is the initial amount , b is the rate of change and t be the time period.

According to the given table , at t=0 hour the exponential function

=f(0)=180 , therefore A =180

At t=1 hour ,the exponential function

[tex]=f(1)=180b^1\\\Rightarrow\ 90=180b\\\Rightarrow\ b=\frac{90}{180}=\frac{1}{2}=0.5[/tex]

Thus by substituting the value of A and b in the function we get the required exponential function =[tex]f(t)=180(0.5)^t[/tex] , where t is the time period.

The exponential function that represents the best relationship between f(t) and t is f(t) = 180(0.5)t.

The following information should be considered:

  • The exponential function should be presented by [tex]f(t) = Ab^t[/tex].
  • Here A denotes the initial amount, b denoted the rate of change, and t denotes the time period.
  • When t = 0, the  exponential function should be f(0) = 180 So A = 180.

Now

[tex]f(1) = 180b^1\\\\90 = 180b\\\\b = 90\div 180 = 0.5[/tex]

Therefore we can conclude that the exponential function that represents the best relationship between f(t) and t is f(t) = 180(0.5)t.

Learn more: brainly.com/question/22271063

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