Find the formula for the exponential function passing through the points

Question

(-3,1/2) & (2,16)?

Answer 1

Given points ( -3 , 1/2 )  ( 2 , 16 )

Let Formula for exponential function is y = ab^x

This equation is passes through each point.

When passes y = ab^x through point ( -3 , 1/2 )

Then

1/2 = ab^-3

1/2 = 1 / ab^-3

2 = ab³   ----------(1)

When passes y = ab^x through point ( 2 , 16 )

Then

16 = ab²    ----------(2)

Equation(1) / Equation(2)

2/16 = ab³ / ab²

b = 1/8

Substitute b = 1/8 in Equation(2)

16 = a(1/8)²

a = 16*8²

a = 1024

Substitute a = 1024 , b = 1/8 in Equation y = ab^x

y = 1024(1/8)^x

y = 1024×8^-x

The exponential function passing through given points is y = 1024×8^-x