Answer: ![y=4(1.75)^x](https://tex.z-dn.net/?f=y%3D4%281.75%29%5Ex)
Step-by-step explanation:
Given graph models a function f which is an exponential function.
We know that the exponential function is given by
, b is the rate of change and x is the time period.
In the given graph we see two points as (0,4) and (1,7)
Now, put x=0 and y=4 (for first point) in the exponential function such that
![4=Ab^0\\\Rightarrow4=A\ or\ A=4](https://tex.z-dn.net/?f=4%3DAb%5E0%5C%5C%5CRightarrow4%3DA%5C%20or%5C%20A%3D4)
Put x=1, y=7 and A=4 (for second point) in the exponential function such that
![7=4b^1\\\Rightarrow7=4b\\\Rightarrow\ b=\frac{7}{4}\\\Rightarrow\ b=1.75](https://tex.z-dn.net/?f=7%3D4b%5E1%5C%5C%5CRightarrow7%3D4b%5C%5C%5CRightarrow%5C%20b%3D%5Cfrac%7B7%7D%7B4%7D%5C%5C%5CRightarrow%5C%20b%3D1.75)
Now substitute A=4 and b=1.75 in the standard exponential function we get our equation that models the given function that predicts the value of a trading card, in hundreds of dollars (y)
, where x is the number of decades.