A power function with form y = ax^p passes through points (2,48) and (3,162).

Question

Find the constants a and p:

a = ________

p = ________

(a step by step would be much appreciated)

Answer 1

Hi Vincent P

I interpret your question as follows:

y = ax^p

Passes through points (2, 48) and (3, 162)

48 = a(2)^p

162 = a(3)^p

You want to find a and p

162/48 = a(3)^p/a(2)^p

Since a is in the numerator and denominator it cancels out

3.375 = (3/2)^p

3.375 = (1.5)^p

We can use logarithms to solve for p, you look up the rules for logarithms in your text or online

log(3.375) = plog(1.5)

log(3.375)/log(1.5) = p

3 = p

Now we can substitute p with one of the given points to solve for a

48 = a(2)³

48 = 8a

48/8 = a

6 = a

Checking with the second point (3, 162)

162 = 6(3)³

162 = 6(27)

162 = 162

I hope this helps.

Answer 2

48 = ax²

162 = ax³

3.375 = x, divide second equatiuon by first

Now substitute into either equation and solve for a