Question

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

0 0.01
1 0.005
2 0.0025
3 0.00125

Answer 1

y = 0.01·(0.5^x)

Explanation:

You want the exponential function that gives the sequence ...

0.01 (for x=0), 0.005, 0.0025, 0.00125

Exponential function

The exponential function can be written ...

y = initial value · (common ratio)^x

The initial value is 0.01. The common ratio is 0.005/0.010 = 0.5.

Using these values in the equation, we have ...

y = 0.01(0.5^x)