Question

Does the function `f(x) = 32(.5^x)` show growth or decay?

Answer 1

As the base `0.5` the base is less than `1`, it shows decay.

Explanation:

See `1.01^2=1.0201`, `1.01^3=1.030301`, `1.01^4=1.04060401`

and `0.99^2=0.9801`, `0.99^3=0.970299`, `0.99^4=0.96059601`

It is observed that even if the base is slightly higher than `1`, there is growth and even if the base is slightly lower than `1`, there is decay. This growth or decay is sharper if the base is farther from `1` on either side.

For `f(x)=32(0.5^x)`, the graph appears as below.

graph{32(0.5^x) [-16.88, 23.12, -7.24, 12.76]}