alrighty
any exponential function can be written in form
y=abˣ
we are given f(1) and f(2)
also g(1) and g(2)
to solve for the equations, we do the following:
f(2)=ab²
f(1)=ab¹
so
f(2)/f(1)=(ab²)/(ab¹)=b=6/2=3
then simple subsitution tells us that a=2/3
[tex]f(x)=(\frac{2}{3})(3)^x[/tex]
for g(x)
g(2)/f(1)=(ab²)/(ab¹)=b=4/2.5=8/5
using experimentaion, we find that
[tex]g(x)=(\frac{25}{16})(\frac{8}{5})^x[/tex]
A. if we solve we get about x=1.3
that is below 1 ad 2
or, we notice that since they are polynomials, they are continous
then make a table to show that f(1)<g(1) and f(2)>g(2) so therefor they intersect somewhere beween x=1 and x=2
B. see above in the begining
