Question

The initial population is 91. The population doubles every 14 years. What is the equation for the population after t number of years?

Answer 1

Geometric progression

Answer 2

Use for formula,
\[\Large T_n = ar^{n-1}\]

Answer 3

Where a is initial popl. i.e. 91.

Answer 4

every 14 years means use \(A_0\times 2^{\frac{t}{14}}\)

Answer 5

n(t)=n0e^kt

Answer 6

n0=initial population

Answer 7

find k then use k to find t

Answer 8

There's probably more that one approach to this, but I think @cammyabbo has the more useful one.

Answer 9

91(2)^(t/14)?

Answer 10

once you have e, you take the ln of both sides to bring down your exponent

Answer 11

182=91e^k(2)

Answer 12

becomes 91=e^k(2)

Answer 13

to hell with the e, too much work

Answer 14

thats wrong

Answer 15

you are told the doubling time, use 2 as the base

Answer 16

2=e^k(2)

Answer 17

take the ln of both sides

Answer 18

ln 2=k(2)

Answer 19

k=ln 2/2 plug back into original equation to find t

Answer 20

I don't remember you quoting a general formula @satellite73

Answer 21

You all have royally confused me. lol

Answer 22

??

Answer 23

follow my posts

Answer 24

you are told the doubling time. doubles every 14 hours right? so it look like this

at time 0 you have 91, at time 14 you have \(91\times 2\) at time 28 you have \(91\times 4=91\times 2^2\) and in general you have \(91\times 2^x\)

Answer 25

now since it doubles every 14 year you know that the exponent should look like \(\frac{t}{14}\) so that if t is a multiple of 14 you get just what you want. now you can make t any value you like
so general formula is
\[91\times 2^{\frac{t}{14}}\]

Answer 26

That's not general enough. I'm referring to a global general math formula that you can apply to any problem. I know you're the man on here, but there's a reason why general formulas were created.

Answer 27

there is no reason not to use 2 as a base if you are doubling

Answer 28

You always seem to neglect posting such general formulas.

Answer 29

ok suppose i have a population that increases by 20% every 3 hours. and lets say i start with P
then instantly i know i can model this as
\[P(1.2)^{\frac{t}{3}}\] what more do i need?

Answer 30

if if the half life is h, i use
\[A_0(\frac{1}{2})^{\frac{t}{h}}\] done

Answer 31

this going back and forth with e is math teacher nonsense inflicted on students for no good reason at least not at this level

Answer 32

You could have posted that general formula at the beginning of your explanation. It helps other users understand your basis of approach

Answer 33

is
\[A_0(\frac{1}{2})^{\frac{t}{h}}\] general ?

Answer 34

but this calls for going straight to the answer using your eyes and head, not a formula
doubling time is 14 years, initial population is 91, use
\[91\times 2^{\frac{t}{14}}\]an explanation might be needed but a general formula is not

Answer 35

I don't know if it is or not, but it's better than just presenting some equation where it looks like you just randomly posted some numbers from the problem and threw an equation together. As far as using eyes and head, you're losing sight on the fact that not every user is as familiar with such things as you are.

Answer 36

You should always post with other users in mind.

Answer 37

That which is so obvious to you may be so confusing for someone else.

Answer 38

@Aprilmbug what numbers were you given?

a) doubles use the number 2 as a base
b) time: 14 years
c) initial population, 91

formula : \(91\times 2^{\frac{t}{14}}\) what could be more straightforward?

Answer 39

randomly posted numbers? i respectfully disagreed. i used only the numbers written above

Answer 40

I could write 2 x 14 divided by 91 = t but that would be misleading, wouldn't it?

Answer 41

compare my formula with the one with the log and the e and all that (which is of course correct, although there is a minor mistake, it should be \(2=e^{14k}\) but no matter

Answer 42

well the math teachers teach us in these ways

Answer 43

im not a math wiz, i have to follow general rules and formulas, otherwise i mess up

Answer 44

and what do you see? a bunch of steps to change the base from 2, which it is because you are givne the doubling time, to the base of e using logs for god sake. why?

Answer 45

that is one way of solving the problem, i hope it helped

Answer 46

Yeahh I just went to wolfram alpha.
but thanks guys