Answer:
Step-by-step explanation:
An exponential function has a standard form
[tex]y=a(b)^x[/tex] where a is the initial value, b is the rate of growth or decay, and x and y are found in coordinates from the table. We need to solve for b, the rate of change (growth or decay). We will use the first 2 coordinates in the table, namely (1, 6) and (2, 4) to solve for b. We will use a system of equations...2 equations for 2 unknowns. The first equation is found by plugging in a 6 for y and a 1 for x to get:
[tex]6=a(b)^1[/tex] and, solved for a:
[tex]a=\frac{6}{b}[/tex].
In the second equation, we will plug in a 4 for y, a 2 for x and the value for a we just found:
[tex]4=\frac{6}{b}(b)^2[/tex] and, simplified a bit:
[tex]4=\frac{6b^2}{b}[/tex] which finally simplifies to
4 = 6b and
[tex]b=\frac{2}{3}[/tex]. That's the rate of change we are asked to find. We could continue to find the whole equation. Plug in 2/3 for b to solve for a:
[tex]a=\frac{6}{\frac{2}{3} }[/tex] and
[tex]a=\frac{6}{1}*\frac{3}{2}=\frac{18}{2}=9[/tex] and the exponential equation is
[tex]y=9(\frac{2}{3})^x[/tex] that means that we started with 9 of something and it is dying/decaying/depreciating at a rate of 33%
