Question

in 1965 a town had a population of 55,000.
in 1995 a town had a population of 89,500.
assuming exponential growth, estimate the population in the year 2005? use A=P(o)e^(kt)

Answer 1

wanna do it the snap way?

Answer 2

rater not do it at all lol... but have to show work.

Answer 3

oh ok then you have to do it the hard way
ready?

Answer 4

we start counting in 1965, so we will make that year zero, and so\(P_0=55,000\)

Answer 5

then we know that our formula will look like
\[A=55,000e^{kt}\] and we need to find \(k\)

Answer 6

how did you get \(k\)?

Answer 7

sorry wrong problem, my mistake

Answer 8

wrong problem as in the question is the wrong problem or as in you solved the wrong problem?

Answer 9

solved the wrong problem..... to find k i found the percentage growth of 55,000 to 89,500 which is 63%

Answer 10

ok if you are going to do that, then it is a different formula

Answer 11

\[89500e ^{.63(15)}\]\[89500e ^{9.45}\] = 1137380791

Answer 12

you would use
\[55,000\times (1.63)^{\frac{t}{30}}\]

Answer 13

if you are using \(e\) as the base, you have to solve for k

Answer 14

thought i was doing something wrong....

Answer 15

\[A=55,000e^{kt}\] and you know \(A=89,500\) when \(t=30\) so you have to solve
\[89,500=55,000e^{30k}\] for k

Answer 16

divide by 55,000 get
\[\frac{179}{110}=e^{30k}\]
\[30k=\ln(\frac{179}{110})\]
\[k=\frac{1}{30}\ln(\frac{179}{110})\]

Answer 17

i get \(.02623\) rounded and now you have your \(k\) and therefore your formula

Answer 18

im getting k=0.016

Answer 19

your way was the snap way, but it doesn't use
\[A=P_0e^{dt}\] as i said you would use
\[A=55,000\times \left(\frac{89,500}{55,000}\right)^{\frac{t}{30}}\]

Answer 20

you are right, i copied wrong

Answer 21

.01623

Answer 22

so it becomes \[A=89500e ^{0.16(15)}\]\[A=895e ^{2.4}=986574.29\]
correct?

Answer 23

from 1995 to 2005 is ten years, not 15

Answer 24

\[A=89500e^{.1623}\]

Answer 25

i get 105,271

Answer 26

mixing up problems again (cant post my actualy problem so crafter a similar one)... thank you

Answer 27

why can't you post the actual one?