Answer:-The multiplicative rate of change for the exponential function =3
Explanation:-
The exponential function is given by ![y=Ab^x](https://tex.z-dn.net/?f=y%3DAb%5Ex)
, where A is the initial amount , b is the rate of growth and x is the time period.
From the given graph ,we can see points on the exponential curve.
For point (0,2), x=0 and y=2
Thus ![y=Ab^x](https://tex.z-dn.net/?f=y%3DAb%5Ex)
![\Rightarrow2=Ab^0\\\Rightarrow2=A(1)\\\Rightarrow\ A=2](https://tex.z-dn.net/?f=%5CRightarrow2%3DAb%5E0%5C%5C%5CRightarrow2%3DA%281%29%5C%5C%5CRightarrow%5C%20A%3D2)
For point (1,6) , x=1 and y=6
![y=Ab^x](https://tex.z-dn.net/?f=y%3DAb%5Ex)
![\Rightarrow6=2b^1\\\Rightarrow3=b\\\Rightarrow\ b=3](https://tex.z-dn.net/?f=%5CRightarrow6%3D2b%5E1%5C%5C%5CRightarrow3%3Db%5C%5C%5CRightarrow%5C%20b%3D3)
OR we can see in the graph y is increasing 3 times the previous value.
Therefore, the multiplicative rate of change for the exponential function =3