Question

X-1 0 1 2 fx 18 6 2 2/3 what is the decay factor of the exponential function represented by the table 1/3 2/3 2 6

Answer 1

Answer:

Step-by-step explanation:

Let's find out algebraically.  It never hurts to practice with these anyways!

The formula for exponential growth/decay is

$y=a(b)^x$ , where a is the intial amount and b is the growth/decay rate.  We will choose 2 points from the table and figure out mathematically what the rate of decay is.  We know it's decay because the y values are decreasing as the x values are increasing.  

We will use the points (0, 6) and (1, 2) to find the model for this situation:

$6=a(b)^0$ and since any number or variable raised to the power of 0 equals 1, then:

a = 6.  We will use that a along with the x and y from the other point we chose and find b, the rate of decay:

$2=6(b)^1$ and

2 = 6b so

$b=\frac{1}{3}$

The rate of decay or decay factor is 1/3.  You could also have looked at the y values and seen that in order to get to the next one down you had to divide by 3...

Whichever way works for you.  But using the data will not fail you when you find what you're looking for algebraically.