Question

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

Answer 1

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Answer 2

The equation of exponential function of following table is represented by $y = A(B^{x})$.

Step-by-step explanation:

Given,

   x        y

   0       0.1

   1       0.05

   2      0.025

   3      0.0125

To find the equation of exponential form.

Exponential form,

y = A($B^{X}$)

Case 1,

y = 0.1, x = 0

$0.1 = A(B^{0} ) \\\\0.1 = A(1)\\\\A = 0.1$

Case 2,

y = 0.05, x = 1

0.05 = 0.1($B^{1}$)

B = 0.5

Case 3,

y = 0.025

x = 2

0.025 = 0.1($B^{2}$)

0.025 = 0.1($0.5^{2}$)

0.025 = 0.1(0.25)

0.025 = 0.025

Case 4,

y = 0.0125

x = 3

0.0125 = 0.1($0.5^{3}$)

0.0125 = 0.1(0.125)

0.0125 = 0.0125

So, we implemented the formula y = A($B^{X}$).

We found the value of A and B, and also proved it in case 3 and case 4.

Therefore, the equation of exponential function of following table is represented by $y = A(B^{x})$.