Question

Find a possible formula for the exponential function?
1.(0,40),(5,15)
2.(-2,12/9),(2,27/4)

Answer 1

I'll do the easy one, then you show me how you did the easy one:

(-2,12/9),(2,27/4)
let the function be y = a(b)^x
case 1: 12/9 = a(b)^-2
case 2: 27/4 = a(b)^2

divide the second by the first:

[a(b)^2] / [a(b)^-2] = (27/4) / (12/9)
b^4 = 81/16
b = ± 3/2
sub back into case 2 equation:
if b = 3/2
27/4 = a(3/2)^2
27/4 = (9/4)a
a = 27/9= 3

if b = -3/2
27/4 = a(-3/2)^2
27/4 =(9/4)a
a = 3

y = 3(±3/2)^x

check: if x = 2
y = 3(9/4) = 27/4

if x = -2
y = 3(4/9) = 12/9 , my answer is correct