Question

During the first month after the opening of a new shopping home, sales were $72 million. Each subsequent month, sales declined by the same fraction. If the sales during the third month after the opening totaled $18 million, what is that fraction?

Answer 1

I need some clarification.

Explanation:

1st month `->` $72 million
3rd month `->` $18 million

I assume that you are saying that every month, the sales drop in this manner:

1st month is $72 million,

(Letting fraction = `x`, )

2nd month is $`72x` million

So 3rd month is $`(72x)x` million = $`18?`

If so, please give me the thumbs up to go ahead..

Because it can also mean a fraction the original $72 million was removed in the 2nd month.

Answer 2

`color(blue)(1/(root(3)(4))`

Explanation:

If we model this on an exponential function:

`A_t=A_0e^(kt)`

`18=72e^(3k)`

`ln(1/4)/3=k`

`A_t=72e^((ln(1/4))^(t/3)`

`A_t=72(1/4)^(t/3)`

`A_t=72(1/(root(3)(4)))^t`

So `(1/(root(3)(4)))` seems to be the fraction we seek.

Testing this:

looking at $18 M. after 3 months.

`18/72=1/4`

We would expect after 6 months the amount to be:

`1/4*18=9/2`

And:

`(1/(root(3)(4)))^6=9/2`

Answer 3

`1/2`

Explanation:

I'm reading the question this way - We have sales in Month 1 of $72M, month 3 of $18M, and an equal fraction decline from months 1 to 2 and 2 to 3. What's that fraction?

The first thing I'd do is to look at the fraction decline from 72 to 18:

`18/72=1/4`

Since this represents the total decline over 2 months, by observation we can see the fraction is `1/2`:

`x^2=1/4=>x=1/2`

Testing this, we should see sales declining by `1/2` each month:

Month 1: `$72M`
Month 2: `1/2xx$72M=$36M`
Month 3: `1/2xx$36M=$18M`