Question

A table of values for an exponential function is

shown.
X
y =
0
1
2
3
4
Y
10
5
2.5
1.25
0.625
Write the equation for the function shown in the table
by typing values in the blank spaces.
) x

Answer 1

One possible equation for the function shown in the table is:

y = 10 * (0.5)^x

This equation represents an exponential function with a base of 0.5 (i.e. each value is half of the previous value) and an initial value of 10 (i.e. y = 10 when x = 0).

To verify this equation, we can plug in the x-values from the table and see if we get the corresponding y-values:

- When x = 0: y = 10 * (0.5)^0 = 10 * 1 = 10 (matches the table)

- When x = 1: y = 10 * (0.5)^1 = 10 * 0.5 = 5 (matches the table)

- When x = 2: y = 10 * (0.5)^2 = 10 * 0.25 = 2.5 (matches the table)

- When x = 3: y = 10 * (0.5)^3 = 10 * 0.125 = 1.25 (matches the table)

- When x = 4: y = 10 * (0.5)^4 = 10 * 0.0625 = 0.625 (matches the table)

Therefore, the equation y = 10 * (0.5)^x represents the function shown in the table.

Hope this helps if can