make an exponential equation for this table

Question

x y
1 12
2 36
3 108
4 324

give it in a form to write on a math paper

Answer 1

To find an exponential equation that fits the data given in the table, we can look for a general form of an exponential equation, which is:

$$y=a\cdot b^x$$

where $a$ and $b$ are constants.

From the values in the table:

| x | y | |---|----| | 1 | 12 | | 2 | 36 | | 3 | 108 | | 4 | 324 |

Let's determine the constants $a$ and $b$:

1. Start with the point when $x=1$: $$y=a\cdot b^1=12$$ Thus, we have: $$a\cdot b=12(1)$$

2. For $x=2$: $$y=a\cdot b^2=36$$ Thus, we have: $$a\cdot b^2=36(2)$$

3. Dividing equation (2) by equation (1): $$\frac{a\cdot b^2}{a\cdot b}=\frac{36}{12}$$ $$b=3$$

4. Now substitute $b=3$ back into equation (1): $$a\cdot 3=12$$ $$a=4$$

Now we have both values:

• $a=4$
• $b=3$

Putting this together, the exponential equation is:

$$\boxed{{\displaystyle y=4\cdot 3^x}}$$

This is the exponential function that corresponds to the data points in your table.