Question

Suppose Q = 38.8(0.829)^t. Give the starting value a, the growth factor b, and the growth rate r if Q = a • b^t = a(1 + r)^t. a =b = r =

Answer 1

we have

`\begin{gathered} Q=38.8(0.829)^t \\ \text{and} \\ Q=a\cdot b^t \end{gathered}`

then:

a = 38.8

b = 0.829

and we have

`\begin{gathered} Q=a\cdot b^t=a(1+r)^t \\ so, \\ b=1+r \\ 0.829=1+r \\ 0.829-1=1+r-1 \\ r=-0.171 \end{gathered}`

r in percentage

`r=0.171*100=17.1`

r = 17.1%

answer:

a = 38.8

b = 0.829

r = - 0.171