In a math question involving growth or decay you use the following formula: y= a (1 +/- r) ^t
"a" is your starting amount. "t" is the amount of time involved. "r" is your rate converted to decimal form. Inside the parentheses you add if it is growth, subtract if it is decay. 1 is the same as 100%, your starting point.
So, the result of (1 - r) is your growth factor. In this case you lose 10%. That is 0.1 in decimal form. 1 - 0.1 = 0.9 which is your growth factor.
When asked questions specifically about interpreting growth factor, just remember that anything above 1 is growth, anything below 1 is decay. So a growth factor of 1.25 would mean a growth rare of 25% or .25
We are given that the annual rate of change is -10%. We are asked if the growth or decay factor is .10.
This is false.
Since the annual rate of change is negative, I would interpret the question as a 10% decrease each year. Then the growth factor would be 1 - 0.1 = 0.9. (Since the "growth factor" is between 0 and 1, we have a decay model—we could also say the decay factor is 0.9.)
Typically, we have a decay model of y = A(1-r)^t where A is the initial amount, r is the decay rate, and t the time in appropriate units. I have interpreted -10% as a 10% decrease: r = 0.1 placed in a decay model. I would not take y = a(1-(-.1))^t as r should be given as a percent greater than zero.
https://www.thoughtco.com/exponential-decay-definition-2312215
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