Question

Find the equation of the exponential function represented by the table below:

2
y
0.1
1
0.05
2
0.025
3 0.0125

Answer 1

The exponential equation is;

y = 0.1•0.5^x

Explanation:

Here, we want to get the exponential function represented by the table

Mathematically, the general form of an exponential function is;

y = a•b^x

By getting a and b, we have the exponential function

We can use any of the points;

Let us start with (0,0.1)

0.1 = a•b^0

anything raised to zero is 1

0.1 = a * 1

a = 0.1

Now, we have a

Let us work with the second point to get b

The point is (1,0.05)

0.05 = 0.1•b^1

0.05 = 0.1b

b = 0.05/0.1

b = 0.5

Thus, we have the equation as;

y = 0.1•0.5^x