Answer:
[tex]f(x) = 2000 * 1.05^x[/tex]
Step-by-step explanation:
The key to this question is interpreting the graph and then modelling it into an exponential function.
You are given 2 key characteristics of this graph. 1 characteristic being that it intercepts the y-axis at (0,2000), and another characteristic being that it goes through the point (1,2100)
Now refer to the standard form of an exponential function.
[tex]y = a * b^x[/tex]
Since you know that when x = 0, y = 2000, a must be 2000. Because [tex]b^0 = 1[/tex], 2000 * 1 = 2000
So you got your a value. Sub it into the equation and now you got.
[tex]y = 2000 * b^x[/tex]
You still need to solve for b, so this is where you do some algebra. Pick your key point, (1,2100), sub in those values for x and y, and solve for b.
[tex]2100 = 2000 * b^1\\\frac{2100}{2000} = b\\ 1.05 = b[/tex]
Now you have your a and b values. Now you can express using a function:
[tex]f(x) = 2000 * 1.05^x[/tex]
