How do you identify equations as exponential growth, exponential decay, linear growth or linear decay #f(x) = 9.6 ∙ 1.06x#?

1 Answer
Oct 7, 2015

Answer:

See explanation below.

Explanation:

A linear expression has a form of #f(x)=ax+b#. It is an increasing function ("growth" as you call it) if #a>0#, if #a<0# then it is a decreasing function ("decay")

An exponential function has a form of #f(x)=a*b^x#, it is usually defined for #b>0#. Such a function is growth if #a>1# or decay if #a in (0;1)#.

So if you meant to write #f(x)=9.6*1.06x#, then it is a linear growth function.

But if you mean a function like:

#f(x)=9.6*(1.06)^x#,

then it is an exponential function, and it is a growth ftnction, because #1.06>1#