Find a formula for the exponential function passing through the points (−2,320) and (1,5)

Question

Find a formula for the exponential function passing through the points (−2,320) and (1,5)

Answer 1

f(x) = 20(1/4)^x

f(1) = 5 = 20(1/4)^1 = 20(1/4) =5

f(-2) = 320 = 20(1/4)^-2 = 20(4)^2 = 20(16) = 320

y=ab^x

5=ab^1 = ab

a =5/b

320=ab^-2

320b^2 = a = 5/b

320b^3 = 5

b^3 = 5/320 = 1/64

b = cube root of 1/64 = 1/4

a = 5/b = 5/(1/4) = 20

y=20(1/4)^x