Question

Y=a(b)^ * contains the points (2, 60) and (3,120 below

Answer 1

The exponential equation that contains points (2, 60) and (3, 120) is y = 15 · 2ˣ.

How to determine an exponential equation

We must derive an exponential equation y = a · bˣ, where a, b are real coefficients, that contains the points (x, y) = (2, 60) and (x, y) = (3, 120). First, build a system of equations with given points:

60 = a · b²

120 = a · b³

Second, find all coefficients:

`(60)/(b^2) = (120)/(b^3)`

60 · b³ = 120 · b²

b = 2

`a = (60)/(2^2)`

a = 15

Third, determine the exponential equation:

y = 15 · 2ˣ

By algebraic handling, the exponential equation is y = 15 · 2ˣ.