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29 April, 20:11

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?

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  1. 29 April, 20:57
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    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
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