Finding a Formula

Question

Find a formula for the exponential function of the form y = a b^x passing through the points (4,-25) and (8,-125). Find exact values for a and b.

 

 

Answer 1

Hi Sally,

 

Given the formula and the two points you've been given, you have two equations:

 

y = a b^x

plug in (4, -25) for (x, y)

-25 = a b⁴

 

plug in (8, -125)

-125 = a b⁸

 

-125 = a b⁸

-25 = a b⁴

 

Divide the first equation by the second. This is legal since a cannot be zero. (If a=0, then -125=0, which isn't true.)

-125/-25 = ab⁸ / ab⁴

 

5 = b⁴

b = 5^1/4 = ⁴√(5)

 

Substitute this back into either equation:

-25 = a (5^1/4)⁴

-25 = a (5)

a = -5

 

y = -5 [⁴√(5)]^x