I'm a little bit confused about stating exponential growth.
We have a growth factor which is stated as 1 + the rate it's growing as a decimal.
So I have a table like this:
x y
1 2
2 6
3 18
4 54
5 162
6 486
I can see that my "y" is growing 3 times each time the "x" goes up by 1, or tripling. So how do I state my growth rate?
If tripling is 300%, that would be 13.00 as a growth rate (1 + the rate as a decimal), but that doesn't come out correctly either -- 54 x 13 = 702, now 162, etc. I'm so confused!
y = 2/3 * 3^x
this isn't a growth factor?
since it triples every year, that's a 200% per year growth rate.
To determine the growth rate in your table, you can identify the pattern by which the "y" value is increasing for each subsequent "x" value. In this case, the "y" values are tripling, as you correctly observed.
To express this as a growth rate, you need to determine the decimal equivalent of tripling.
Starting with a base value of 1, if you triple it, you would multiply by 3. Therefore, the growth factor would be 3, not 13.
To state the growth rate as a decimal, you would subtract 1 from the growth factor and express it as a decimal. In this case, it would be 3 - 1 = 2.
Thus, the growth rate for this exponential growth pattern is 2 (or 200% as a percentage).
Now let's test this growth rate with your table:
Starting with a y-value of 2, when we multiply by the growth rate of 2, we should get the next value.
2 x 2 = 4 (not 6).
However, this does not match the next value in your table. It seems that there is an error in the table or the growth pattern you are observing.
Please double-check the values in your table or provide the correct values to analyze the growth rate accurately.