Answer:
see explanation
Step-by-step explanation:
The equation of the exponential function in the form
y = a[tex]b^{x}[/tex]
Substitute the given points into the equation and solve for a and b
Using (1, 7.5), then
7.5 = ab → (1)
Using (3, 16.875), then
16.875 = ab³ → (2)
Divide (2) by (1)
[tex]\frac{ab^3}{ab}[/tex] = [tex]\frac{16.875}{7.5}[/tex], hence
b² = 2.25 ( take the square root of both sides )
b = 1.5
Substitute b = 1.5 into (1)
1.5a = 7.5 ⇒ a = 5
The exponential function is y = 5[tex](1.5)^{x}[/tex]
