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 bamboo shoot, what are the values of a and b
Answers
Answer:
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.
Step-by-step explanation:
please mark me as braienliest
Answer:
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}
3
x
then the height of the bamboo shot becomes:
y=5(2)^{\frac{x}{3}}y=5(2)
3
x
⇒y = 5(\sqrt[3]{2})^xy=5(
3
2
)
x
On comparing with [1] we have;
⇒a = 5 ina=5in and b = \sqrt[3]{2}b=
3
2
Therefore, the value of a = 5 and b = \sqrt[3]{2}b=
3
2