Answer:
![24576=3(2)^{m-1}](https://tex.z-dn.net/?f=24576%3D3%282%29%5E%7Bm-1%7D)
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. = ![a_n=ar^{m-1}](https://tex.z-dn.net/?f=a_n%3Dar%5E%7Bm-1%7D)
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,![24576=3(2)^{m-1}](https://tex.z-dn.net/?f=24576%3D3%282%29%5E%7Bm-1%7D)
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![24576=3(2)^{m-1}](https://tex.z-dn.net/?f=24576%3D3%282%29%5E%7Bm-1%7D)