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) 100 50 25


Which exponential function best represents the relationship between f(t) and t?

f(t) = 0.5(100)t

f(t) = 100 (0.25)t

f(t) = 0.25(50)t

f(t) = 100(0.5)t

Answer 1

In this problem, we are given with the points (0, 100) and (1, 50) and (2,25) and is asked in the problem which among the functions correctly fit to the points. Via reverse engineering, we substitute the points to the functions and see which of them fits to the points. In this case, the answer to this problem is D. f(t) = 100(0.5)^t 

Answer 2

Answer:
`f(t)=100(0.5)^t`

Explanation:

We know that the exponential function is represented as

`f(t)=Ab^t`, where A is the initial amount and b is the multiplicative rate of change and t is the time period.

In the given situation, at t=0, f(t)=100, thus A=100

Now, put A=100 and t=1 in the above equation we get

`f(1)=100b^1\\\Rightarrow50=100b\\\Rightarrow\ b=(1)/(2)\\\Rightarrow\ b=0.5`

Thus, the exponential function best represents the relationship between f(t) and t is ,
`f(t)=100(0.5)^t`