Question

A power function with the form y=aᵖ passes through the points (3, 486) and (5, 6250). What are the values of a and p?

Answer 1

To find the values of a and p in the power function y=aᵖ, we can substitute the given points and solve the equations simultaneously. The values of a and p are 6 and 3, respectively.

Step-by-step explanation:

We are given two points on a power function with the form y=aᵖ as (3, 486) and (5, 6250). Let's use these points to find the values of a and p.

1. First, we'll substitute the x and y values from the first point into the equation to form the equation 486=a³.
2. Next, we'll substitute the x and y values from the second point into the equation to form the equation 6250=a⁵.
3. Now, we can solve these equations simultaneously to find the values of a and p. Dividing the second equation by the first equation gives a²=a². Simplifying further, we find a=6.
4. Finally, substituting the value of a into one of the original equations, a³=486, we can solve for p. Taking the cube root of both sides gives p=3.

Therefore, the values of a and p are 6 and 3, respectively.