Find the Exponential function

Question

...That passes through the points (1,162) and (3,18) in the form f(x)= A *B^x.

Answer 1

f(x) = y = AB^x

18 = AB^3 (eq 1)

162 = AB^1 (eq 2)

Divide eq 1 by eq 2

18/162 = 1/9 = B^2

B = 1/3

y = A(1/3)^x

using eq 2 (easier) 162 = A(1/3)^1

162 = (1/3)A

A = 3(162) = 486

y = 486(1/3)^x

Check with eq 1

18 =? 486(1/3)^3

18 =? 486(1/27)

18(27) = 486 check

f(x) = 486(1/3)^x

Answer 2

f(x) = AB^x; f(3) = AB³ = 18; f(1) = AB = 162; B² = 1/9; B = 1/3 (B > 0); A = 486; f(x) = 486·(1/3)^x

Answer 3

162 = ab¹

18 = ab³

Divice top equation by bottom equation to determine b

Substitute b into either equation to determine a