Answer: [tex]y=4(1.75)^x[/tex]
Step-by-step explanation:
Given graph models a function f which is an exponential function.
We know that the exponential function is given by
[tex]y=Ab^x[/tex], 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
[tex]4=Ab^0\\\Rightarrow4=A\ or\ A=4[/tex]
Put x=1, y=7 and A=4 (for second point) in the exponential function such that
[tex]7=4b^1\\\Rightarrow7=4b\\\Rightarrow\ b=\frac{7}{4}\\\Rightarrow\ b=1.75[/tex]
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)
[tex]y=4(1.75)^x[/tex], where x is the number of decades.
