Respuesta :
Answer:
13
Step-by-step explanation:
Let's start by creating the beginning of the data sample, knowing the volume doubles every minute.
Min 0 = 3
Min 1 = 6
Min 2 = 12
Min 3 = 24
Min 4 = 48
If we look at the numbers, we see they are all divided by 3:
Min 0 = 3 / 3 = 1
Min 1 = 6 / 3 = 2
Min 2 = 12 / 3 = 4
Min 3 = 24 / 3 = 8
Min 4 = 48 / 3 = 16
We then see the result of the division by 3 is in fact the table of multiplication by 2.
So, by inverting the operation, we can see the volume of air for any given minute starting from now is 3 times 2 at the power of the minute (m).
[tex]x = 3 * 2^{m}[/tex]
We then have to isolate m knowing x.
[tex]24576 = 3 * 2^{m}[/tex]
[tex]8192= 2^{m}[/tex]
Which power of 2 = 8192? 13 (0=1,2,4,8,16,32,64,128,256,512,1024,2048,4096,13=8192)
Answer:
[tex]24576=3(2)^{m-1}[/tex]
Step-by-step explanation:
Given : Ari is filling a one-man hot-air balloon. He starts with only 3 cubic feet of air in the balloon and observes that the volume doubles every minute.
To Find: What equation can be used to find the number of minutes, m, it will take for the volume to reach a capacity of 24,576 cubic feet of air?
Solution:
Ari starts with only 3 cubic feet of air in the balloon and observes that the volume doubles every minute.
Let m be the number of minutes
The given situation forms G.P.
Formula of nth term in G.P. = [tex]a_n=ar^{m-1}[/tex]
a is the first term = 3 cubic feet
r is the common ratio =2
We are required to find equation can be used to find the number of minutes, m, it will take for the volume to reach a capacity of 24,576 feet3 of air
So,[tex]24576=3(2)^{m-1}[/tex]
Hence equation can be used to find the number of minutes, m, it will take for the volume to reach a capacity of 24,576 cubic feet of air is[tex]24576=3(2)^{m-1}[/tex]
