exponential functions

Question

Find a formula for the exponential function passing through the points  and 

Thank you so much!

Answer 1

general form of exponential equation: y = ab^x

Using the given points:

(−2,32): 32 = ab^-2

(1,4): 4 = ab¹

Dividing the first equation by the second gives:

8 = b^-3

Solve for b:

b = 8^-1/3 = .5

Plug b into one of the equations to solve for a:

4 = ab¹ = a(.5)¹

a = 4 / .5 = 8

Plug a and b into the equation:

y = 8(.5)^x

Answer 2

y = ab^x, Point (- 2, 32) give us equation : 32 = ab^-2 and point (1, 4) give us 4 = ab¹ = ab. From here a = 4/b

and 1st equation 32 = 4b^-3; b³ = 1/8; b = (1/8)^1/3 = 1/2 and a = 4/(1/2) = 8.

So this exponential function y = 8(1/2)^x