Answer:
4. f(x) = 200(1/2)^x
Step-by-step explanation:
We can determine the function which matches the relationship shown in the table easily by simply inputting the values.
1. f(x) = 100/x
f(1) = 100/1 = 100
f(2) = 100/2 = 50
f(3) = 100/3 = 33.33 NOT 25
function 1 does not match
2. f(x) = 100(1/2)^x
f(1) = 100(1/2)^1 = 50 NOT 100
function 2 does not match
3. f(x) = 50(2)^x
f(1) = 50(2)^1 = 100
f(2) = 50(2)^2 = 200 NOT 50
function 3 does not match
4. f(x) = 200(1/2)^x
f(1) = 200(1/2)^1 = 100
f(2) = 200(1/2)^2 = 50
f(3) = 200(1/2)^3 = 25
f(4) = 200(1/2)^4 = 12.5
f(5) = 200(1/2)^5 = 6.25
function 4 does match
Therefore, the function that models the relationship shown in the table is function 4: f(x) = 200(1/2)^x.
