Question

Write an exponential function y=ab^x for the graph that includes (-3,16) and (-1,4)

Answer 1

16=ab^(-3) and
4=ab^(-1)
remember
(x^m)/(x^n)=x^(m-n)
also
x^-m=1/(x^m)

divide first equation by 2nd
16/4=(ab^(-3))/(ab^(-1))
4=b^(-3-(-1))
4=b^(-3+1)
4=b^(-2)
4=1/(b^2)
times both sides by b^2
4b^2=a
divide both sides by 4
b^2=1/4
sqrt bth sides
b=1/2

sub back

4=ab^-1
4=a(1/2)^-1
4=a(1/(1/2))
4=a(2)
divide both sides by 2
2=a

the funtino is


`y=2( (1)/(2))^x`

Answer 2

Answer: f(x)=2(0.5)^x