Answer:
y = [tex]\frac{1}{8}[/tex][tex](2)^{x}[/tex]
Step-by-step explanation:
For an exponential of the form y = a[tex](b)^{x}[/tex]
Use the given points to find a and b
Using (3, 1 ), then
1 = ab³ → (1)
Using (5, 4 ), then
4 = a[tex]b^{5}[/tex] → (2)
Divide (2) by (1)
[tex]\frac{ab^5}{ab^3}[/tex] = 4
b² = 4 ⇒ b = [tex]\sqrt{4}[/tex] = 2
Substitute b = 2 into (1)
a2³ = 1
8a = 1 ( divide both sides by 8 )
a = [tex]\frac{1}{8}[/tex]
Thus exponential function is
y = [tex]\frac{1}{8}[/tex][tex](2)^{x}[/tex]
