Answer:
y = 3[tex](2)^{x}[/tex]
Step-by-step explanation:
Substitute the given points into the function and solve for a and b
Using (2, 12)
12 = ab² → (1)
Using (5, 96)
96 = a[tex]b^{5}[/tex] → (2)
Divide (2) by (1)
[tex]\frac{ab^5}{ab^2}[/tex] = [tex]\frac{96}{12}[/tex] , that is
b³ = 8 ( take the cube root of both sides )
b = [tex]\sqrt[3]{8}[/tex] = 2
Substitute b = 2 into (1) and solve for a
12 = a2² = 4a ( divide both sides by 4 )
3 = a
Thus
y = 3[tex](2)^{x}[/tex] ← is the exponential function
