Find a formula for the exponential function passing through the points ( − 3 , 6250 ) and ( 2 , 2 )

Question

can someone please explain how to do this

Answer 1

y = a(b)^x

Since (2,2) is on the graph, 2 = ab² and since (-3, 6250) is on the graph, 6250 = ab^-3.

From the first equation, a = 2/b².

Substitute in to the other equation to get 6250 = (2/b²)(b^-3)

So, 3125 = b^-5

b⁵ = 1/3125

Therefore, b = 1/5 and a = 2/b² = 50

The equation is y = 50(1/5)^x