Find the formula for an exponential function that passes through the two points given. Please show work. (-1,3/4) and (3,192)?

The exponential function is: y = abˣ

where b > 0

When x = -1, y = 3/4:

3/4 = ab⁻¹

ab⁻¹ = 3/4 …… [1]

When x = 3, y = 192:

192 = ab³

ab³ = 192 …… [2]

[2]/[1]: b⁴ = 256

b = 4

Substitute b = 4 into [2]:

a * 4³ = 192

64a = 192

a= 3

The exponential function is: y = 3 * 4ˣ

I don't know.................

you have only 2 points, so there are an infinite number of solutions, and a straight line or other curves also are solutions.

try y = Ax² + B

plug in the numbers, solve for A and B

y = Ax² + B

3/4 = A + B

192 = 9A + B

subtract

191.25 = 8A

A = 23.90625

B = 0.75–23.90625 = –23.15625

so equation is

y = 23.90625 x² – 23.15625

check

x = –1

y = 0.75

x = 3

y = 192