Answer:
Step-by-step explanation:
To find the exponential function represented by the given table, we can use the general form of an exponential function:
y = a * b^x
where:
y is the dependent variable (the values in the table)
x is the independent variable (the inputs in the table)
a is the initial value when x = 0
b is the base of the exponential function (the common ratio)
Let's use the values from the table to find the exponential function:
For x = 0, y = 0.02. This gives us the initial value, a = 0.02.
For x = 1, y = 0.01. Plugging these values into the exponential function, we get:
0.01 = a * b^1
Substituting the value of a, we have:
0.01 = 0.02 * b
Solving for b, we divide both sides by 0.02:
b = 0.01 / 0.02 = 0.5
For x = 2, y = 0.005. Plugging these values into the exponential function, we get:
0.005 = a * b^2
Substituting the values of a and b, we have:
0.005 = 0.02 * 0.5^2
Simplifying, we get:
0.005 = 0.02 * 0.25
Solving for a, we divide both sides by 0.02:
a = 0.005 / 0.25 = 0.02
Therefore, the exponential function represented by the given table is:
y = 0.02 * (0.5)^x
