Question

Determine whether the function represents exponential growth or exponential decay.$f\left(t\right)=\frac{1}{3}\left(1.26\right)^t$

Answer 1

For an exponential function of the form:

`y=a\cdot b^x`

a = Initial value

b = growth factor = 1 + r

r = Rate of change

So:

`\begin{gathered} f(t)=(1)/(3)(1.26)^t \\ b=1+r=1.26 \\ so\colon \\ r=1.26-1 \\ r=(1.26-1)*100 \\ r=26 \end{gathered}`

Answer:

26%