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

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:

Now

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.

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- The exponential function best represents the relationship between f(t) and t is

Explanation:-

The exponential function is given by , 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

Thus by substituting the value of A and b in the function we get the required exponential function = , where t is the time period.