Question

The table represents an exponential function.

What is the multiplicative rate of change of the function?

Answer 1

Explanation:

All we are doing here is solving for the b in

`y=a(b)^x`, which is the standard form for an exponential function.

Use the first 2 coordinate pairs to solve for b: (1, 6) and (2, 4):

`6=a(b)^1` so

`a=(6)/(b)` and use that when you write the next equation using the next coordinate pair:

`4=(6)/(b)(b)^2` which simplifies to

4 = 6b so

`b=(2)/(3)`, the second choice there. Another way of saying multiplicative rate is the rate of decay or the rate of growth. Same thing. This is decay since 2/3 is greater than 0 but less than 1.