SOLUTION: In 1997, there were 43.2 million people who used free weights. Assuming the use of free weights increases 6% annually, which equation can be used to predict the number of people us

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Question 1038459: In 1997, there were 43.2 million people who used free weights. Assuming the use of free weights increases 6% annually, which equation can be used to predict the number of people using free weights t years from 1997?
p = 43.2(0.06)^t
p = 43.2(1.06)^t
p = 43.2(0.94)^t
p = 43.2(1.005)^t
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The amount next year is always the amount this year plus 6% times the amount this year.

So lets look at what happens the first couple of years. Since t is the number of years after 1997, in 1997, t = 0, in 1998, t = 1, and so on. 
   t     Previous       Amount Added           Total
-------------------------------------------------------------------------------------------------------------------
   0      0             43.2                    0    +  43.2
   1      43.2          43.2(0.06)             43.2  +  43.2(0.06) = 43.2(1.06)
   2      43.2(1.06)    [43.2(1.06)](0.06)     43.2(1.06) + 43.2(1.06)(0.06) = 43.2(1.06)(1.06) = 43.2(1.06)²

I'll leave it to you to verify that for the total is .

So, if we use the facts that and for any real numbers , then we can clean up our chart thus: 
   t        Total
-----------------------------
   0        43.2(1.06)^0
   1        43.2(1.06)^1
   2        43.2(1.06)^2
   3        43.2(1.06)^3
        .
        .
        .
   n        43.2(1.06)^n


John

My calculator said it, I believe it, that settles it