A power function with form y = ax^p passes through points (3, 8/243) and (5, 8/3125).

Question

Find the constants a and p

a = ______________

p = ______________

Answer 1

p=-5

a = 8

y =8x^-5

y = 8/x⁵

(3,8/243) = (3, 8/3^5)

(5, 8/3125) = (5,8/5^5)

8/243 = a3^p

8/3125 =a5^p

two equations, two unknowns,

solve for a and p

8/3^5 = a3^p

a = 8(3^(5+p))

8/5^5 = a5^p

a = 8(5^(5+p))

3^(5+p) = 5^(5+p)

5+p=0

p=-5

a=8/(3^0)= 8/(5^0) 8/1 = 8

y=ax^p

y = 8x^-5