Question

Hi I need help on a few problems. I have been trying to do them but I can't seem to get the correct answer.

1. A population P is initially 2000. Find an exponential model (growth or decay) for the population after t years if the population P is increases by 400% every 3 years. (Round your terms to two decimal places.)

P(t)= ?


2. A population P is initially 2000. Find an exponential model (growth or decay) for the population after t years if the population P is multiplied by 0.85 every month. (Round your terms to four decimal places.)

P(t)= ???

Answer 1

http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/ is a great explanation of exponential growth

Answer 2

\[a*e^{rt}\] where r = rate and t = time, rate is in percentage

Answer 3

a is you initial amount (parameter)

Answer 4

that's alot i'm still confuse

Answer 5

\[2000e^{(400/3)t}\]

Answer 6

I recommend that site for this, its the best explanation for exponential growth ive seen

Answer 7

2000e^{(400/3)t} is wrong apparently

Answer 8

it says you have to round your terms so the fraction would need to be expressed as a decimal to two places

Answer 9

do you mind explaining me it

Answer 10

http://www.mathsisfun.com/algebra/exponential-growth.html is another good site

Answer 11

I will try my best, so the reason that we have this number "e" is because this growth is "continual" meaning that it is compounded continuously. are you familiar with the concept of something being compounded continually?

Answer 12

yeah kinda

Answer 13

In the context of this problem what "compounded continuously" means is that the population is increasing across ever interval of time. It is not the case that after 3 years the population magically jumps 400% but as people are born it increases faster as those new to the population have kids and their kids have kids and so forth. Basically each new person is available to create more people so the growth is "non linear" meaning it follows a curve, meaning it grows faster and faster as time goes on.

Answer 14

\[e= \lim_{n \rightarrow \infty} (1+1/n)^n\], this mathematically means that e is the value by which something compounded continuously grows in one unit of time.

Answer 15

sorry i was typing my answer in the wrong box it was right. can you help me with the second problem please

Answer 16

yes but i have to be breif because im at work, check out those web sites for a better explination. 2) \[2000e^{.85(12)t}\]

Answer 17

ok thanks