# shearing 2584 sheep who reproduce at rate of 7.6% every 2 years

#### thouchen

##### New member
I have 2584 sheep. They re-produce at a rate of 7.6% every 2 years. I can shear only 48 sheep per year. How many years will it take to shear all of my sheep?

But, this is a very real problem that I could really use your help with. I used to be pretty good at math, but I've been using my brain to solve problems that are less mathematical and more societal over the years. By helping me, you might be helping to save lives.

I have 2584 unsheltered homeless persons living in homeless encampments in my county. The most recent Point-in-Time Survey (homeless census) indicated a 7.6% increase over the past 2 years. Only 48 people will be housed this year. Using the same rate of increase and the same number of persons housed, how many years will it take my county to house every homeless person.

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#### Subhotosh Khan

##### Super Moderator
Staff member
I have 2584 sheep. They re-produce at a rate of 7.6% every 2 years. I can shear only 48 sheep per year. How many years will it take to shear all of my sheep?
How many sheeps are added to your flock first year? second year?

#### tkhunny

##### Moderator
Staff member
Ummm... You do know that the wool grows back, right? You will NEVER shear them all, particularly if there are no deaths. This is a terrible problem statement.

#### thouchen

##### New member
How many sheeps are added to your flock first year? second year?
340 every other year

#### thouchen

##### New member
You are all probably right.

So, I'll put it in the actual terms of my math problem. I was very good at math many years ago. Unfortunately, I've become victimized by society causing my brain to be concerned with solving other problems that are not always mathematical. But, in this case it is and I could use some help.

There are 2584 unsheltered homeless persons living in my county. The most recent bi-annual Point-in-Time Survey (homeless census) showed an increase of 7.6% in the number of homeless over the past 2 years. This year only 48 homeless people will become housed. Using the same rate of increased homeless population and the same number housed each year in the future in the future, How many years will it take to get them all in housing?

#### tkhunny

##### Moderator
Staff member
It ALWAYS helps to give the correct information up front, rather than trying to disguise your efforts.

Okay, the first thing you need to do it get your information on the same page. An annual housing rate and a biannual increase rate is no good.

$$\displaystyle \sqrt{1.076} = 1.0373$$ - Use an ANNUAL rate of increase of 3.73%.

Here' few years for you...

 Population Housed New Start 5,984 Year 1 6,159 48 223 Year 2 6,341 48 230 3 6,530 48 237 4 6,725 48 244 5 6,928 48 251 6 7,138 48 258 7 7,357 48 266 8 7,583 48 274 9 7,818 48 283

As can be seen, we are falling behind. Your society will have to do better if people are to be housed.