Answer:
[tex]y = 750 \cdot (0.98)^x[/tex]
Step-by-step explanation:
The most basic form of an exponential function in (x, y) is
y = a · bˣ [1]
where a and b are constants
We can solve for the exponential function as follows:
We see from the table that at x = 0, y = 750
Plugging these values into the equation [1] we get
y₀ = a · b⁰ = 750
→ a · b⁰ = 750
and since b⁰ = 1
a = 750
So the equation is of the form
y = 750bˣ
Now let's take another point given to us in the table
x = 10, y = 600
Plug these values into equation [2]
y₁₀ = 750 b¹⁰ = 600
or
750 b¹⁰ = 600
b¹⁰ = 600/750 = 0.8
b = tenth root of 0.8 = [tex]\sqrt[10]{0.8} \approx 0.98[/tex]
So the exponential equation for the given table is
[tex]y = 750 \cdot (0.98)^x[/tex]
The provided image shows the points indicated on the table as well as the function graph
