Find a formula for the exponential function passing through the points (-1, 3/2 ) and (1,6)

Question

Find a formula for the exponential function passing through the points (-1, 3/2 ) and (1,6)

show how so i can atleast learn from it too

Answer 1

So A = IB^t. You have two points of the form (t, A). Plug the points into the equation to get two separate equations.

3/2 = IB^-1 and

6 = IB¹

Solve the systems of equations, giving you I and B.

I good way of doing this is multiply the equations together. (They teach you to solve systems of equations by adding and subtracting the equations, but you can also multiply them, which works beautifully in this case)

(3/2) x 6 = (IB^-1)(IB¹)

9 = I² or I = 3.

Next solve for B by plugging I back into the equation

6 = IB. Therefore B = 2

So, the equation is A = 3 x 2^t