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?

Answer: [tex]y=180(0.5)^x[/tex]Step-by-step explanation:The general exponential function is written as :-[tex]y=Ab^x--------------(i)[/tex],where y is the amount of the material after t years , A is the initial amount and b is the multiplicative rate of growth or decay.From the given table , f(0)=180Thus the  initial value of radioactive material  =180Also, the decay factor is the ratio of the consecutive terms :[tex]b=\dfrac{90}{180}=0.5[/tex]Now, put A = 180 and b =0.5 in (i), we get[tex]y=180(0.5)^x[/tex]Therefore, the exponential function best represents the relationship between f(t) and t is [tex]y=180(0.5)^x[/tex]