Question

Find a power function of the form y=ax^b whose graph passes throught the points (2, 5) and (8, 12).

How do i solve this??

Answer 1

sub in the two points to get two equations
5 = a(2)^b
12=a(8)^b

divide one by the other
12/5 = 8^b/2^b
2^3b / 2^b = 2.4
2^2b = 2.4
log 2^2b = log 2.4
2b = log2.4/log2
b = .631517..
sub back into
5 = a(2^.631517)
a = 3.2275

so y = 3.2275(x^.631517)

check:
if x = 2 , y = 3.2275(2^.631517) = 5
if x=8 , y = 3.2275(8^.631517) = 1.9999998
not bad!