Write an exponential function y = abx for a graph that passes through (2, 1) and (3, 12).

Question

help

Answer 1

y=ab^x

plug in the points (2,1), (3,12) for (x,y)

1=ab^2

12=ab^3

divide last equation by 2nd equation

12/1 = ab^3/ab^2=b

b=12

a=1/b^2=1/12^2=1/144

f(x)=(1/144)12^x

is the exponential function through the given points

where a= 1/144 and b= 12 in f(x)=ab^x

check the answer

plug in the points again

y=12^x/144

1= 12^2/144 = 144/144= 1

12 = 12^3/144 =12^2(12)/144 = 144(12)/144 = 12

this doesn't look like a problem you'd find in an "algebra 1" course, which is the category it's listed under. Not even an honors algebra 1 course.