Question

What is the equation of the exponential function `y=ab^x` passing through the points `(2,3.84)` and `(3, 3.072)`?

Answer 1

Taken you to where you should be able to finish it.

Explanation:

We are given two condition resulting in

For point `P_1->(x,y)=(2,3.384)->3.84=ab^(2)" "...Equation(1)`

For point `P_2->(x,y)=(3,3.072)->3.073=ab^(3)" "...Equation(2)`

Initial step is to combine these in such a way that we 'get rid' of one of the unknowns.

I choose to 'get rid' of `a`

`3.84/b^2=a" "...................Equation(1_a)`
`3.073/b^3 =a" "................Equation(2_a)`

Equate them to each other through `a`

`3.84/b^2=a=3.073/b^3`

`b^3/b^2= 3.073/3.84`

`b= 3.073/3.84`

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You should be able to solve for `a` now by substituting for `b`