Respuesta :
Answer:
its 152 i know cause i just did this....
Step-by-step explanation:
Answer:
An exponential function is in the general form [tex]\mathrm{y}=\mathrm{a}(\mathrm{b})^{\mathrm{x}}[/tex]
Explanation:
(x,y) = (-1,4/3) and (x,y)= (3,108) are the given functions
Therefore,
[tex]\frac{4}{3}=a(b)^{-1}=\frac{a}{b}[/tex]
[tex]\frac{4}{3}=\frac{a}{b}[/tex] - eq(1)
[tex]108=a(b)^{3}=a b^{3}=108-e q(2)[/tex]
Multiply both sides of the first equation by b to find that
[tex]\frac{4}{3} b=a[/tex]
Substituting in eq-2 we get
[tex]\frac{4}{3} b^{4}=108[/tex]
[tex]b^{4}=81[/tex]
[tex]\mathrm{b}=\pm 3[/tex]
[tex]\mathrm{b}=+3, \text { then } 108=\mathrm{a}(3)^{3}[/tex]
which gives a = 4,
henceforth the equation becomes as [tex]\mathrm{y}=4(3)^{\mathrm{x}}[/tex]
[tex]\mathrm{b}=-3 \text { then } 108=\mathrm{a}(-3)^{3}[/tex]
which gives a = -4,
henceforth the equation becomes as y = [tex]-4(-3)^{x}[/tex]
However! In an exponential function, b>0, otherwise many issues arise when trying to graph the function.
The only valid function is [tex]4(3)^{x}[/tex]
