Question #cc09c

1 Answer
Jan 30, 2018

The next number is 25.

The formula is

#y=200(1/2)^x, x in NN#


This is an exponential decay or half-life type of question. The number halves each time, so the number after 50 is 25.

The general equation for exponential decay can be expressed as


where #a# is the initial amount, and #b# is the base. In this case we want a base of 1/2, because the number is halving each time.

If the number sequence was 200, 50, 12.5, etc. we would use a base of 1/4 because the number is being quartered each time. The initial amount can also be any number, but in this case #a=200#. Plugging these into the equation, we get

#y=200(1/2)^x, x in NN#

#NN# are the natural numbers (positive integers including zero).

Notice that we had to restrict the values that #x# can take because there are a discrete number of values that we want. For example, #x# can't be 1.5, because that would give a number that is not one of our answers.

The graph looks like this

The important thing here is that #x# can only take on whole number values, which is why we restricted the domain to natural numbers. The line drawn through the points is only there because I don't know how to turn it off.