Question

Find the equation of the exponential function represented by the table below:

xx yy
0 4
1 16
2 64
3 256

Answer 1

y = 4·4^x

Explanation:

We can write the exponential function in the form ...

y = a·b^x

The y-value for x=0 is 4, so that is the multiplier 'a' in our equation.

The ratio of values between x=1 and x=0 is 16/4 = 4, so that is the value of 'b' in the equation. The equation is ...

y = 4·4^x

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Additional comment

This could also be written ...

y = 4^(x+1)

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Consider the values for x=0 and x=1.

x=0: y = a·b^0 = a

x=1: y = a·b^1 = ab

Then the ratio of values is (ab)/(a) = b.

This is the fact that we used in the above working.