Question

Write an exponential function in the form y = ab* that goes through points (0,12) and (2,768).

Answer 1

The exponential function is $y=12(8)^{x}$

Step-by-step explanation:

The form of the exponential function is $y=ab^{x}$ , where

• a is the value of y when x = 0
• b is the rate of change

∵ The form of the exponential function is $y=ab^{x}$

∵ The function goes through points (0 , 12) and (2 , 768)

- Substitute the coordinates of the first point to find the value of a

∵ x = 0 and y = 12

∴ $12=ab^{0}$

∵ $b^{0}=1$

∴ 12 = a(1)

∴ a = 12

Substitute the value of a in the form of the function

∴ $y=12(b)^{x}$

- Substitute the coordinates of the second point to find the value of b

∵ x = 2 and y = 768

∴ $768=12(b)^{2}$

- Divide both sides by 12

∴ 64 = b²

- Take √ for both sides

∴ b = 8

- Substitute the value of b in the form of the function

∴ $y=12(8)^{x}$

The exponential function is $y=12(8)^{x}$

Learn more:

You can learn more about the logarithmic function in brainly.com/question/1447265

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