2. Section 11.2
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The equation of an exponential function is y=ab^x. The given points must satisfy the equation.
y=4(1.5)^x
We want to write an exponential function for the graph that passes through the given points. Let's consider the general form for this type of a function.
y=ab^x
Since we want the points to lie on the graph, they must both satisfy this equation. By substituting these points into the formula, we get two equations.
(I): a^1=a
(I): Rearrange equation
(I): .LHS /b.=.RHS /b.
(II): a= 6/b
(II): a/c* b = a* b/c
(II): Simplify quotient
(II): Rearrange equation
(II): .LHS /6.=.RHS /6.
(II): sqrt(LHS)=sqrt(RHS)
(II): b > 0
Having solved for b, we can substitute this into the first equation to find a.
Finally, we can write the full equation of the exponential function. y=4(1.5)^x