How would I find the formual of power function out of these 2 point? (5,75)(10,600)
To find the formula of a power function given two points, you can use the following steps:
Step 1: Write down the general form of a power function, which is:
y = k * x^n
Step 2: Substitute the x and y values of the first point (5, 75) into the equation to obtain:
75 = k * 5^n
Step 3: Substitute the x and y values of the second point (10, 600) into the equation to obtain:
600 = k * 10^n
Step 4: Divide the second equation by the first equation to eliminate k:
600 / 75 = (k * 10^n) / (k * 5^n)
Simplifying this equation gives:
8 = 2^n
Step 5: Solve for n by taking the logarithm of both sides of the equation:
log 8 = log 2^n
Using the logarithmic property log a^b = b * log a, we can rewrite the equation as:
log 8 = n * log 2
Step 6: Solve for n by dividing both sides of the equation by log 2:
n = log 8 / log 2
Using a calculator, evaluate the right side of the equation to find the value of n.
Step 7: Substitute the value of n into one of the original equations (e.g., the first equation) to solve for k:
75 = k * 5^(n value)
Solve this equation for k.
Step 8: Substitute the values of k and n into the general form of the power function to get the final formula:
y = (k value) * x^(n value)
By following these steps, you can find the formula of the power function given the two points (5, 75) and (10, 600).