Question

Find a formula for the exponential function passing through the points (-1,5/3) and (3, 135).

Answer 1

The expression y = 4.998 · $e^{1.098\cdot x}$ is the exponential function that passes through the points (- 1, 5 / 3) and (3, 135).

How to derive an exponential function that passes through two given points

Herein we find the location of two points set on Cartesian plane that belongs to an exponential function of the form:

$y = A \cdot e^{B \cdot x}$

Where:

• A - y-Intercept of the exponential function.
• B - Growth factor
• x - Independent variable.
• y - Dependent variable.

Which is equivalent to the following logarithmic expression:

㏑ y = ㏑ A + B · x

If we know that (x₁, y₁) = (- 1, 5 / 3) and (x₂, y₂) = (3, 135), then the following system of equations is generated:

㏑ (5 / 3) = ㏑ A - B

㏑ 135 = ln A + 3 · B

Then, we solve the system by numerical methods:

㏑ A = 1.609 (A = 4.998), B = 1.098

And the exponential function is equal to y = 4.998 · $e^{1.098\cdot x}$.

To learn more on exponential functions: brainly.com/question/11487261

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