Question

Which graph best shows the function f(x)=3(3)-x to represent the rate at which a radioactive substance decays

Graph A
Graph B
Graph C
Graph D

Answer 1

Answer:Graph C

Explanation:

Enter the function on desmos graphing and it will show you that it is C

Answer 2

`f(x)=3(3)^(-x)=3\left((1)/(3)\right)^x=\left((1)/(3)\right)^(x-1)`



`f(x)=a^x\\if\ a\in(0;\ 1)\ then\ a\ function\ is\ decreasing\\if\ a > 1\ then\ a\ function\ is\ increasing`


`f(x)=\left((1)/(3)\right)^(x-1)\to a=(1)/(3)\in(0;\ 1)\\The\ function\ is\ decreasing`


`f(0)=\left((1)/(3)\right)^(0-1)=\left((1)/(3)\right)^(-1)=3^1=3\to(0;\ 3)`

Answer: Graph C.