Question

Find the exponential equation that passes through each pair of points.show your work. (-1,-2)and (3,-162)

Answer 1

The exponential equation is $y=-6(3)^{x}$

Step-by-step explanation:

The form of the exponential function is $y=a(b)^{x}$ , where

• a is the value of y at x = 0
• b is the exponential factor

∵ The exponential function passes through point (-1 , -2)

∴ x = -1 and y = -2

- Substitute them in the form of the equation

∵ $y=a(b)^{x}$

∴ $-2=a(b)^{-1}$

- Remember $b^{-1}=\frac{1}{b}$

∴ $-2=a(\frac{1}{b})$

- Multiply both sides by b

∴ -2 b = a

- Switch the two sides

∴ a = -2 b

∵ The exponential function passes through point (3 , -162)

∴ x = 3 and y = -162

- Substitute them in the form of the equation

∵ $-162=a(b)^{3}$

- Substitute a by -2 b

∴ $-162=-2b(b)^{3}$

- Divide both sides by -2

∴ $81=b(b)^{3}$

- Remember $b.b^{x}=b^{x+1}$ , when we multiply same

   bases we add their exponents

∵ $b.b^{3}=b^{3+1}$

∴ $b.b^{3}=b^{4}$

- Substitute it in the equation

∴ $81=(b)^{4}$

- Take $\sqrt[4]{}$ for both sides

∴ b = 3

- Substitute the value of b in a = -2 b to find a

∵ a = -2 b

∴ a = -2(3)

∴ a = -6

- Substitute the values of a and b in the form of the exponential

   equations above

∴ $y=-6(3)^{x}$

The exponential equation is $y=-6(3)^{x}$

Learn more:

You can learn more about the logarithmic function in brainly.com/question/11921476

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