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 \ \