Question

The data in the table can be modeled using an exponential function.

x | -1 | 0 | 1 | 2 | 3 |
y | 4 | 6 | 9 | 13.5 | 20.25 |

Based on the table, which function represents the same relationship?

A.) f(x) = 6 x 1.5^x
B.) f(x) = 0.67^x
C.) f(x) = 4 x 1.5^x
D.) f(x) = 6 x 0.67^x

Answer 1

A

Explanation:

You can plug in the x and y coordinates of the points to check which one is right.

The easiest point to start with is (0, 6).

`A) 6=6*1.5^0\\B) 6=0.67^0\\C) 6=4*1.5^0\\D) 6=6*0.67^0`

Any number raised to the power of 0 is 1, so we can replace all of the exponents with 1.

`A) 6=6\\B) 6=1\\C) 6=4\\D) 6=6`

That means we can immediately rule out B and C, since 6 clearly does not equal 1 or 4.

But since we still don't have our answer, we can plug in another point. Once again, you want to start with low, easy numbers, so let's plug in (1, 9).

`A) 9=6*1.5^1\\D) 9=6*0.67^1`

Any number raised to the power of 1 is the same number:

`A) 9=6*1.5\\D) 9=6*0.67`

Now we can multiply out both sides:

`A) 9=9\\D)9=4`

Once again, it becomes immediately clear that D does not work, and A is therefore the correct equation.