Answer:
[tex]f(x)=100(\frac{3}{5} )^x[/tex]
Step-by-step explanation:
Since the exponential function approaches y=0, its equation is of the form,
[tex]f(x)=a(b^x)[/tex]
The point (0,100) is this graph so it must satisfy its equation
[tex]100=a*b^0[/tex]
[tex]100=a(1)[/tex]
a=100
The equation now becomes:
[tex]f(x)=100*b^x[/tex]
We now substitute the point (1,60)
[tex]60=100*b^1[/tex]
[tex]b=\frac{60}{100} =\frac{3}{5}[/tex]
Therefore the required equation is [tex]f(x)=100(\frac{3}{5} )^x[/tex]
