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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?

2 Answers

3 votes

Answer:

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}

User Abhishek Salian
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8.5k points
3 votes
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
User Enes Zor
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7.7k points