Question

Find the equation of the exponential function represented by the table below 0 0.02 1 0.06 2 0.18 3 0.54

Answer 1

To find the equation of the exponential function represented by the given table, we can use the formula for exponential functions in the form of y = ab^x, where "a" represents the initial value when x = 0 and "b" represents the common ratio.

From the given table, we can see that when x = 0, y = 0.02. This gives us the value of "a" in the equation.

Therefore, a = 0.02.

Now, let's find the common ratio "b" by comparing the values of x and y in the table.

When x = 1, y = 0.06.
When x = 2, y = 0.18.
When x = 3, y = 0.54.

We can see that the ratio of y-values is the same for consecutive x-values:

0.06/0.02 = 0.18/0.06 = 0.54/0.18 = 3.

Therefore, the common ratio "b" in the equation is 3.

Now, we can plug in the values of "a" and "b" into the equation to find the exponential function:

y = ab^x.
y = 0.02 * 3^x.

So, the equation of the exponential function represented by the table is y = 0.02 * 3^x.