Question

In year one, a company earned $3,000 in profits; in year two they earned $9,000 in profits. In year 3 they earned $27,000 in profits and in year 4 they earned $81,000. Whichof the following analytical models illustrates this situation?

Answer 1

Ok, so

We could call "y" to the earnigs, and "x", to the years.

What we're going to do is just replace our values in each option and notice if they are correct or not. Right?

Option A.

`y=3^x`

Replacing the values of x:

`\begin{gathered} y(1)=3^1=3 \\ y(2)=3^2=9 \\ y(3)=3^3=27 \\ y(4)=3^4=81 \end{gathered}`

As you can see, the values are not $3,000, $9,000, $27,000 and $81,000.

Option B.

`y=3x^2`

Replacing the values of x:

`\begin{gathered} y(1)=3(1)^2=3 \\ y(2)=3(2)^2=12 \\ y(3)=3(3)^2=27 \\ y(4)=3(4)^2=64 \end{gathered}`

As you can see, the values are not $3,000, $9,000, $27,000 and $81,000.

Option C.

`y=3x^3`

Replacing the values of x:

`\begin{gathered} y(1)=3(1)^3=3 \\ y(2)=3(2)^3=24 \\ y(3)=3(3)^3=81 \\ y(4)=3(4)^3=192 \end{gathered}`

As you can see, the values are not $3,000, $9,000, $27,000 and $81,000.

Finally, no one of the expressions is correct.

I think that the correct expression, must be this one:

`y=1000(3^x)`

If you check, we would obtain the correct values for the earnings.