Question

A table of values is shown.

X
0
1
2
3
4
Y
y =
-2
-10
-50
- 250
- 1250
Write the equation for the function shown in the table
by typing values in the blank spaces.
)x

Answer 1

The function is an exponential function of the form y = a * b^x, where "a" is the initial value and "b" is the common ratio.

Using the given table, we can see that:

- The initial value is y(0) = -2, so a = -2.

- To find the common ratio, we can divide any term by the previous term. For example:

- b = y(1)/y(0) = (-10)/(-2) = 5

- b = y(2)/y(1) = (-50)/(-10) = 5

- and so on.

Since we get the same value of b for all the ratios, we can conclude that the common ratio is b = 5.

Therefore, the equation for the function shown in the table is: y = -2 * 5^x.