Learning Resources

Investigation 11: Rice or Gold?

Test yourself

Find the function f(x) that describes the data in the following table and use this function  to find f(10).

The successive range values for f(x) have a common ratio, viz. 2. Thus the function is exponential with base of 2. 

If we rewrite the range values as powers of 2, we can see the relation between x and the exponent. This is shown below:

It should be clear that the exponent of the base is always 1 more than the value of x. We can thus write the function as:

f(x) = 2^{x + 1}

We can now use this to evaluate any value of the function for any domain value. Thus:

f(10) = 2^{10 + 1} = 2¹¹ = 2048