Question

**Fan for help**
Suppose the population of a town is 500,000 in 1990. The population increases at a rate of 5% every five years. What will be the population of the town in 2005? Round your answer to the nearest whole number.

I set up the equation to find future population as P(1+r)^t but I keep getting lost and can't find decide if the answer is t=3 or r=.05....please help!

Answer 1

"The population increases at a rate of 5% every five years"

"P(1+r)^t"

What did you use for "r"?

Answer 2

rate

Answer 3

Not enough information. What "rate" did you use?

Answer 4

I couldn't figure it out honestly. I just read the question and wrote down everything I thought needed to be there and worked it into a equation. I didn't leave any information out, the question here appears exactly as it does on my paper. I found a post from a while ago with this same problem and they had a similar problem http://openstudy.com/study#/updates/51e9b718e4b0c98e49ee5981

Answer 5

they also used "r" so I thought I was on the right track....

Answer 6

You need a rate that will do 5% in 5 years.

You MIGHT be tempted to say 5%/5 = 1%, so r = 0.01. This would be wrong, since \(1.01^{5} = 1.0510100501\) and that is greater than 5% in 5 years.

You need a rate that comes out exactly 5% in 5 years. Try \((1+r)^{5} = 1.05\). This gives \(r = 1.05^{1/5} - 1 = 0.00980579767\). Well, THAT's not a very pleasant number. Can we avoid it?

Alternatively, you can play with 't', rather than r. Try \(P(t) = P_{0}(1.05)^{t/5}\). Notice how this gives exactly 5% every 5 years.

Answer 7

So was I even close when I said t=3 because without doing much of anything I was thinking about a 15 year period / by 5% which would be 3 and if I couldn't find the answer I was simply going tom put 3. And 3 was also mentioned in the other post, but 3 makes no since when talking about the population. I just cannot comprehend word problems.

Answer 8

"Word Problems" are not evil. It is just a matter of translating the intent. Sometimes, the translation is like any other foreign language translation. You just have to learn the new language.

2005 = 1990 + 15, t = 15. Depending on exactly what you are doing, it may be fine to use t = 3 -- as long as you are saying that is 3 "5-year periods". That is kind of what you were saying, so you get a "good work" for that. I didn't set it up that way, but you should see it, anyway, as part of my intermediate calculations.

With \(P(t) = P_{0}(1.05)^{t/5}\), we have \(P(15) = 500000\cdot(1.05)^{15/5} = 578,812.5\). Well, not everyone likes half a people, rounding gives 578,813.

Answer 9

Okay, thank you for your time and patience it really helps a lot!

Answer 10

Patience. From me? Not needed. Patience with yourself will help a lot. :-)