Question

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 1

Answer:
`y=180(0.5)^x`

Explanation:

The general exponential function is written as :-

`y=Ab^x--------------(i)`

,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)=180

Thus the initial value of radioactive material =180

Also, the decay factor is the ratio of the consecutive terms :

`b=(90)/(180)=0.5`

Now, put A = 180 and b =0.5 in (i), we get

`y=180(0.5)^x`

Therefore, the exponential function best represents the relationship between f(t) and t is
`y=180(0.5)^x`