Question

Table to Exponential Function

Answer 1

9514 1404 393

Answer:

  y = 0.2·0.5^x

Step-by-step explanation:

The form of an exponential function is ...

  y = a·b^x

If you look at the values of this for x=0 and x=1, you find ...

For x=0

  y = a·b^0 = a·1 = a

The table tells us the corresponding value of y is 0.2, so ...

  a = 0.2

For x=1

  y = a·b^1 = ab

For the given value of a and the table value of y for x=1, we have ...

  0.1 = 0.2·b

  b = 0.1/0.2 = 1/2 = 0.5

Then the exponential function that describes the table is ...

  y = 0.2·0.5^x