exponential functions

Question

An exponential function, in the for f(x)=ab^x, passes through the points (2,5) and (4,180). Find b.

Answer 1

f(x)=ab^x passes through (2,5) and (4,180)

y=ab^x

5=ab^2

180=ab^4

a=5/b^2

a=180/b^4

a=5/b^2

multiply both 5 and b^2 by b^2

you get a=5b^2/b^4

so, 5b^2/b^4=180/b^4

therefore, 5b^2=180

b^2=180/5

b^2=36

factor or take the square root of both sides

b^2=36

b^2-36=0

(b-6)(b+6)=0

b-6=0 or b+6=0

b=6 or b=-6

√b^2=√36

b=±6