Given the table represents the relation between x and y
We need to find which function represents the table
We can find this by substitute with x at the given function and compare the results with the value given in the table :
From the table : at x = 0 , y = 40
Substitute with x = 0 at the options :
Option A : f(x) = (1/4) * 40^x
when x = 0 , f(x) = 1/4 * 40^0 = 1/4
Option B : f(x) = 40 * (1/4)^x
when x = 0 , f(x) = 40 * 1 = 40
Option C : f(x) = 1/2 * 40^x
when x = 0 , f(x) = 1/2 * 1 = 1/2
Option D : f(x) = 4 * (1/3)^x
when x = 0 , f(x) = 4 * 1 = 4
so, compare the results
so, the answer is option B
[tex]f(x)=40\cdot(\frac{1}{4})^x[/tex]
