Question

Modeling exponentials

Answer 1

The population of an endangered bird is decreasing at a rate of .075%per year. There are currently 200,000 of the birds. Write a function that models the bird population. How many birds will their be in 100 years?

Answer 2

A=P(1+r)^nt

Answer 3

\[200,000(1+.075)^{100}\]

Answer 4

Look right?

Answer 5

I found my error...

Answer 6

Problem with formulas is, in 10 years, you'll forget it and won't know how to Solve the problem. Learn to solve without the formula and remember forever

Answer 7

I put (1+.075) needs to be (1-.075) right?

Answer 8

I never said anything Was wrong, Doesn't mean there isn't anything wrong

Answer 9

Well, they are decreasing.. and I got like 248,000, redid it and now I got 200,000... teach me your ways math wizard *^*

Answer 10

This problem is a counting problem. So we have to count Except we don't really Want to count all the way to 100. We just want to count the first few then observe the pattern.

Answer 11

Got you

Answer 12

So currently these are 200,000 birds. We'll call that year zero.

Answer 13

Then subtract .075%?

Answer 14

So I subtract 7.5 for each year?

Answer 15

Which after a 100 years would be 7,500?

Answer 16

Well, the decrease is happening exponentially

Answer 17

Which means, very quickly?

Answer 18

Would it kinda be like.. 7.5 for year one then 7.5+.075% for year two, and so on and so forth?

Answer 19

Sorry, I try to do calculations in my head a lot.

Answer 20

How’d that work?

Answer 21

Wait... .075% of the birds that die would be 150 in the first year. Not 7.5

Answer 22

YOU're confusing the number Let me work on this.

Answer 23

I’m so lost... okay...

Answer 24

Okay?

Answer 25

Yeah, just use the formula, but make sure it is the correct one.

Answer 26

1-r is the decay rate

Answer 27

Makes sense.

Answer 28

BTW, in case you were wondering about the correct formula it is:

\[200000(1-0.00075)^{100}\]

Answer 29

I’m wondering something else now.

Answer 30

What is that?

Answer 31

Why is the decimal so small?

Answer 32

Because .075 is already small to begin with but when you say .075% You're taking a decimal that is already Small and making it even smaller.