Answer:
C
Step-by-step explanation:
The exponential function has standard form
y = a [tex]b^{x}[/tex]
Use the 2 given points to find a and b
Using (3, 182.25) , then
182.25 = a b³ → (1)
Using (2, 202.5) , then
202.5 = ab² → (2)
Divide (1) by (2)
[tex]\frac{ab^3}{ab^2}[/tex] = [tex]\frac{182.25}{202.5}[/tex]
b = 0.9
Substitute b = 0.9 into (1) and solve for a
182.25 = a (0.9)³ ( divide both sides by (0.9)³
a = [tex]\frac{182.25}{(0.9)^3}[/tex] = 250
Thus
f(x) = 250 × [tex](0.9)^{x}[/tex] ← third option
