Answer:
Given the equations:
....[1]
where,
a is the initial amount
b is the growth rate.
x is the number of doubling period and
y represents the height of the bamboo shoot.
As per the statement:
A 5 inch tall bamboo shoot doubles in height every 3 days.
⇒y(0)=a= 5 inch
doubles in height every 3 days
then
in 1 days =

then the height of the bamboo shot becomes:

⇒
![y = 5(\sqrt[3]{2})^x](https://img.qammunity.org/2017/formulas/mathematics/high-school/qckv98jkijak53xqirq74lxv8ex34zi7nh.png)
On comparing with [1] we have;
⇒
and
![b = \sqrt[3]{2}](https://img.qammunity.org/2017/formulas/mathematics/high-school/w7lhv4bvtuu88usx49lljcnpt8zr6wk85s.png)
Therefore, the value of a = 5 and
![b = \sqrt[3]{2}](https://img.qammunity.org/2017/formulas/mathematics/high-school/w7lhv4bvtuu88usx49lljcnpt8zr6wk85s.png)