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?
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
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 = \(\frac{x}{3}\)
then the height of the bamboo shot becomes:
\(y=5(2)^{\frac{x}{3}}\)
⇒\(y = 5(\sqrt[3]{2})^x\)
On comparing with [1] we have;
⇒\(a = 5 in\) and \(b = \sqrt[3]{2}\)
Therefore, the value of a = 5 and \(b = \sqrt[3]{2}\)