Percentage decrease qestion

Can anybody help me with how to go about answering this question?
The number of wasps in a garden decreases by x% each year. Given that the number of wasps halves in 11 year, work out the value of x to one decimal place.
Thanks for anyhelp.

What answer does the mark scheme give? I want to be ok before I tell you how to start.

I don't have any access to a mark scheme unfortunately, it's a questions in a homework booklet.

well

You know how percentage loss works?

say the number of wasps at the start was 100, and say that the "multiplier" for the percentage change was Y


Doing 100 * Y^11 (since 11 years) = 50

Try to work out Y and see how you can turn Y into a percentage value. The Value of Y you should get would be less than 1 since it's percentage loss.

I understand what your saying in terms of finding out y as a multiplier and then putting it to the power of eleven (to represent the years). But having not been given an orginal amount, I dont get how to test if after elevn years the number has decreased by 50%.

because there is one thing that's definite about the statement

Any value will be halved exactly after year 11 years.

I've gotten an answer for this question and I can assure you, any value will, if it corresponds to that certain value of X.

100 * Y^11 (since 11 years) = 50

Y^11 (since 11 years) = 50/100
Y^11 (since 11 years) = 0.5
square root 11 both sides
y = 0.938930....


is that right

yes.

Now see how you can turn that value into percentage.

okay so because it is a decrease in amount, do you do 100 - 0.93....
and get a decrease of 7 percent?

You don’t subtract it from 100. You do 1-0.93... then multiply that by 100. Since it’s asking for 1dp the value of y should be 6.1