The graphs below show four functions: Graph A shows function f of x equals 5 multiplied by 2 to the power of negative x. Graph B shows function f of x equals 5 multiplied by 2 to the power of x. Graph C shows function f of x equals 10 to the power of x. Graph D shows function f of x equals 10 to the power of negative x. Which graph best shows the function f (x) = 5 (2) - x to represent the rate at which a radioactive substance decays?

We are to find the graph which best represents the given function:

f (x) = 5 (2) ^-x

To be able to solve this, let us write the function of each graph mathematically and select the correct one.

Graph A:

function f of x equals 5 multiplied by 2 to the power of negative x = > f (x) = 5 (2) ^-x

Graph B:

function f of x equals 5 multiplied by 2 to the power of x = > f (x) = 5 (2) ^x

Graph C:

function f of x equals 10 to the power of x = > f (x) = 10^x

Graph D:

function f of x equals 10 to the power of negative x = > f (x) = 10^-x

Therefore based on the mathematical interpretations above, only Graph A is similar to the given function. Hence the correct answer is:

Graph A