There are only 7000 people left on earth because of Zombie attacks. We are losing our population at the rate of 5% a day. How many days until there are only 20 people left on earth.

So we set up up decay equation with :

20 = 7000 x (.95)^x

then
(.95)^x = 20 / 7000


x = log (20 / 7000) / log(.95)

Our exponent equals the log of the result then

we need to divide it by the log (.95) because we must convert it to that

base and our answer is 114.2

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Say that we wanted to know how many zombies there would be after 10 days, we would say

n = 7000 x (.95)¹⁰

and then solve for n.

.95 ^ 10 = .5987 so we should have about 59% of our population left

7000 x (.95)¹⁰ = 4191.15

Note : even though we took away 5% for ten years it was still less than 50% of the original population because the 5% ,after the first year, were taken from the remaining part of the population.

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Suppose that there were 2000 people in a retirement home we were closing. We were losing 10% of the people a year. How many years would it be until we had 20 left?

20 = 2000 x (.90)^x

.90^x = .01

x = log(.01)/log(.90) and the answer is 43 years