OpenStudy (anonymous):

A population of rhinos decreases by 22% each year. How many rhinos will there be in 4 years if there are 200 rhinos now?

4 years ago
OpenStudy (tkhunny):

Answer this: How many rhinos will there be NEXT year if there are 200 rhinos now?

4 years ago
OpenStudy (anonymous):

I dont know.... i dont get this

4 years ago
OpenStudy (tkhunny):

That's not good enough, KitKat151. Let's relax a little and wade through it. What is 22% of 200.

4 years ago
OpenStudy (tkhunny):

200*22% = 200 * 0.22 = 44 -- That is exactly correct. Next question. How much is left of 200 after 22% is removed?

4 years ago
OpenStudy (anonymous):

156

4 years ago
OpenStudy (tkhunny):

200 - 44 = 156. Perfect. Now, let's play with this a little. There is another way to do this. We can manipulate the percentage instead of the numbers! We want to remove 22%. This must mean that we will have 100% - 22% = 78% left. Does this make sense?

4 years ago
OpenStudy (anonymous):

Yes!!

4 years ago
OpenStudy (tkhunny):

Okay, then instead of going to all the trouble to calculate how many rhinos to subtract, let's just calculate the value of remaining rhinos directly. How many rhinos are left of 200 if we remove 22%? Hard Way: 200 * 22% = 44 200 - 44 = 156 Smoother Way 200 * 78% = 156 -- Bam!! What do you thnk?

4 years ago
OpenStudy (anonymous):

I think u r awsome!! THANK YOU!!! i get it know! lol

4 years ago
OpenStudy (tkhunny):

What did you get for the 22% reduction for all five years?

4 years ago
OpenStudy (anonymous):

after one year population decreases by 22% => after one year population = population*[1- 22/100] after 2 years population = population*[1- 22/100]^2 after 4 years population = population*[1- 22/100]^4 final population = 200 * (0.78^4) = 74.03

4 years ago
OpenStudy (anonymous):

I got 57.74348736 for 5 years @tkhunny

4 years ago
OpenStudy (anonymous):

Thank you @sriramreddy

4 years ago
OpenStudy (tkhunny):

\(200\cdot(1 - 0.22)^{4} = 200\cdot 0.78^{4} = 200\cdot 0.37015056 = 74.030112\) \(200\cdot 0.78^{5} = 57.74348736\) You are now the exponentially decreasing population wizard!

4 years ago
OpenStudy (anonymous):

THANK YOU!!!!!! lol :)

4 years ago
OpenStudy (tkhunny):

Except, of course, that rhinos don't come in pieces. The correct answer, after four years, most likely would be 74.

4 years ago