Question

A 5 inch tall bamboo shoot doubles in height every 3 days. If the equation y=ab^x, where x is the number of doubling periods, represents the height of the bamboo shoot, what are the values of a and b?

Answer 1

Given the equations:

`y=ab^x` ....[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 =
`(x)/(3)`

then the height of the bamboo shot becomes:

`y=5(2)^{(x)/(3)}`

⇒
`y = 5(\sqrt[3]{2})^x`

On comparing with [1] we have;

⇒
`a = 5 in` and
`b = \sqrt[3]{2}`

Therefore, the value of a = 5 and
`b = \sqrt[3]{2}`

Answer 2

The correct answer for the question that is being presented above is this one: "x = 2; a = 5; b = 3" A 5 inch tall bamboo shoot doubles in height every 3 days. If the equation y=ab^x, where x is the number of doubling periods, represents the height of the bamboo shoot