Suppose the population in a town has an average growth rate of 18% . If there are 15,500 people now living in town, in about how many years will the population grow to 30,000? Use the equation 30,000 = (15,500)(1.18)x and round the value of x to the nearest year.

- anonymous

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- Theloshua

|dw:1440806804136:dw|

- Theloshua

is that the equation you meant to put? its a squared?

- anonymous

um yeah you drew it right.

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## More answers

- Theloshua

okay. do you have any answer choices, or no? and did you attempt to solve it yet?

- anonymous

I do have choices, but I don't know how to solve it with steps. I don't want to just generate it from a calculator... I wanna know how to do it.

- anonymous

Do you want my options?

- Theloshua

yes please :)

- Theloshua

just to double check myself

- anonymous

a. 7
b. 4
c. 6
d. 5

- Theloshua

okay, just a second please

- anonymous

okay

- Theloshua

okay

- Theloshua

The only real way possible is to solve using a calculator, but I will show you how the steps work

- anonymous

okay

- Theloshua

first thing you will do is divide the 15500 from both sides so:|dw:1440807637374:dw|

- Theloshua

good so far?

- anonymous

yeah it canceled out

- Theloshua

okay, now is where your graphing calculator comes in. you must use the function (ln) to solve.

- Theloshua

so \[\ln \left( 30000/15500 \right) = .66\]

- Theloshua

understand so far?

- anonymous

I don't have a graphing calculator on me right now but I understand

- Theloshua

okay good :) then you move on to the other side and use \[\ln (1.18) = .166\]

- anonymous

okay

- Theloshua

so now you have \[.66 = .166x\]

- Theloshua

guess what your next step is ;)

- anonymous

um solve for x?

- Theloshua

so? how do you do that?

- anonymous

I would do
66/100 166/100 x
so 2*3*11/2^2*5^2 2*83/2^3*5^3 x
330/83 which is like 3.975 ish

- anonymous

so my answer would be 4

- anonymous

... I think lol

- Theloshua

whoah.... idk what you just did there... all you had to do was|dw:1440808526563:dw|

- Theloshua

you got the answer, but whatever you did was super complicated

- anonymous

well that's how my book has others solved for x, but I mean I still got the answer. It makes sense to me

- anonymous

You way is simpler so I'll use that way too

- anonymous

sorry what it that number under the 1st . 66 ?

- Theloshua

okay haha, yeah, whenever the equation is set up like that it is easiest to just divide both sides by the number with the variable. it instantly gives yoy your answer

- anonymous

just .166 ?

- Theloshua

yes, .166
both sides are divided by the number with the variable attached to it

- anonymous

okay thank you so much for helping... you are the best!

- Theloshua

okay :D glad I could be of assistance!!!

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