Tutor.com Exponential and Logarithmic Functions Session

Apr. 24, 2012

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Session Transcript - Math - Algebra II, 4/19/2012 9:26PM - Tutor.comSession Date: 4/19/2012 9:26PM
Length: 29.2 minute(s)
Subject: Math - Algebra II


System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)
[00:00:00] The population of a city in 1990 was 1, 215, 112. The population was growing at a rate of about 5% per decade. Predict the population of the city a) in the year 2000 b) in the year 2005
[00:00:00] Hi

Santiago P (Tutor)
[00:00:25] HI. Welcome to tutor.com . how are you?

Guest (Customer)
[00:00:33] Good. I think this is growth

Santiago P (Tutor)
[00:00:49] OK. Can you give me a moment while I take a look at your question?

Guest (Customer)
[00:01:10] Sure

Santiago P (Tutor)
[00:01:38] OK So, you need to predict the population for years 2000 and 2005, right?

Guest (Customer)
[00:02:33] Yes.

Santiago P (Tutor)
[00:02:40] OK. Wow, nice problem! Have you already worked on it, or you don't know how to start?

Guest (Customer)
[00:02:48] dont know how to start

Santiago P (Tutor)
[00:02:58] OK. Then let's get started.

Guest (Customer)
[00:03:23] Great

Santiago P (Tutor)
[00:03:44] Mmmm, it looks like a exponential increase problem, we can do it if we first write an equation, then calculate the population.

Guest (Customer)
[00:04:04] Ok

Santiago P (Tutor)
[00:04:07] Mmmm, do you remember what's the general form of an exponential equation?

Guest (Customer)
[00:04:47] No

Santiago P (Tutor)
[00:04:57] OK. Let me show you. It is...

Guest (Customer)
[00:05:01] Ok, thanks!
[00:05:30] y= a(b)^x?

Santiago P (Tutor)
[00:05:38] Yeah!

Guest (Customer)
[00:05:45] Ok, thanks!
[00:06:09] what is it for decay?

Santiago P (Tutor)
[00:06:29] Could you please rephrase your question?

Guest (Customer)
[00:06:34] the equation

Santiago P (Tutor)
[00:07:01] Ah, in this formula, a is the initial value for x = 0, and b is the rate of increasing.
[00:07:12] All we have to do is find the values of a and b.

Guest (Customer)
[00:07:25] Ok- if this was a decay problem would it be the same equation- I am asking?

Santiago P (Tutor)
[00:07:46] Ahh, yes, it would be the same equation, except that x would be negative.

Guest (Customer)
[00:07:53] Great, thanks

Santiago P (Tutor)
[00:08:15] OK. According to the problem, population in 1990 was 1,225,112, right?

Guest (Customer)
[00:08:19] Yes

Santiago P (Tutor)
[00:08:49] OK. As time starts counting in 1990, we can consider it as the year 0.

Guest (Customer)
[00:09:00] Oo
[00:09:02] *Ok

Santiago P (Tutor)
[00:09:06] So, for 1990, x = 0, and a is 1,225,112.
[00:09:28] Do you follow me so far?

Guest (Customer)
[00:10:01] Yes

Santiago P (Tutor)
[00:10:25] OK. Now, problem says that the popuolation grows at a rate of 5% every decade, right?

Guest (Customer)
[00:10:33] Yes

Santiago P (Tutor)
[00:10:45] OK. How would you express this 5% as a decimal?

Guest (Customer)
[00:11:02] 0.05
[00:11:19] Is this similar to a compound interest problem?

Santiago P (Tutor)
[00:11:39] Yeah. precisely!

Guest (Customer)
[00:11:58]

Santiago P (Tutor)
[00:12:39] As it's saying it's growing, we can add 1 to this value, so, the new population would be the old population, mukltiplied by 1.05 for each decade.
[00:12:45] So, b = 1.05.

Guest (Customer)
[00:13:14] Ok- what does the " a and b"mean again?
[00:13:23] 1+ 0/05
[00:13:28] *1+ 0/05

Santiago P (Tutor)
[00:13:51] a is the initial value for x = 0, and b is the rate of increasing.

Guest (Customer)
[00:14:09] Ok- thanks!

Santiago P (Tutor)
[00:14:20] OK. So, our formula would be...
[00:15:08] Where y is the new population, and x is measured in decades (periods of ten years).
[00:15:25] Do you follow me so far?

Guest (Customer)
[00:15:42] Kinda of- so we need to mention 10 yrs bc of 1900-200
[00:15:46] *2000

Santiago P (Tutor)
[00:16:00] Right, so, for year 2000, x = 1.

Guest (Customer)
[00:16:12] Ok

Santiago P (Tutor)
[00:16:23] So, all we have to do now is make x = 1 in the formula, and calculate the value of y.

Guest (Customer)
[00:16:46] Ok

Santiago P (Tutor)
[00:16:56] OK. So, would you like to give it a try?

Guest (Customer)
[00:17:49] so I multiply 10?

Santiago P (Tutor)
[00:18:20] Mmmm, not exactly. All we have to do is make 1.05^1, then multiply by 1215112.

Guest (Customer)
[00:18:28] what about the 10?

Santiago P (Tutor)
[00:18:40] Which 10?

Guest (Customer)
[00:18:47] from 1900-2000

Santiago P (Tutor)
[00:19:24] Oh, remember that x is in decades. So, for year 2000, there is a difference of 10 years, this is, 1 decade.
[00:19:41] This is why we consider x = 1.

Guest (Customer)
[00:20:09] Ok so just multiply 1215112*1.05?

Santiago P (Tutor)
[00:20:16] Right!

Guest (Customer)
[00:20:36] 1275867.6

Santiago P (Tutor)
[00:20:48] Great!! Nicely done!
[00:21:07] So, population in year 2000 was about 1,275,868. Nicely done!

Guest (Customer)
[00:21:33] but how we never we even used the 10 portion why?

Santiago P (Tutor)
[00:22:21] As I told you above, from 1990 to 2000, there is a difference of 1 decade. Remember that we're treating the x as decades, not years.

Guest (Customer)
[00:22:38] OHHHHH- I did not catch that- THANK YOU!!!!!!!!!!!

Santiago P (Tutor)
[00:22:57] OK, great! Now for the year 2005.

Guest (Customer)
[00:23:18] 1215112*1.05*15?

Santiago P (Tutor)
[00:23:44] Almost there. From 2005 to 1990, ther is a difference of 15 years, this is 1.5 decades.
[00:23:51] So, x = 1.5.

Guest (Customer)
[00:23:50] Oh!
[00:24:21] 1822668

Santiago P (Tutor)
[00:25:01] I'm getting something different. May you please show me how you got that?

Guest (Customer)
[00:25:20] 1215112 (1.5)

Santiago P (Tutor)
[00:25:49] Mmmm, not exactly. You can do it if you make (1.05)^1.5, then multiply by 1215112.
[00:26:29] So, would you like to try again?

Guest (Customer)
[00:26:33] Sure, why 1.05?

Santiago P (Tutor)
[00:26:50] Because it's the rate of increasing we found.

Guest (Customer)
[00:27:19] 1307375.250

Santiago P (Tutor)
[00:27:25] You got it!

Guest (Customer)
[00:27:28] yayay!!

Santiago P (Tutor)
[00:27:49] So, it would be 1.307,375 the population. Fantastic job!
[00:28:05] So, d have any questions about anything we went over today?

Guest (Customer)
[00:28:43] No, but thank you very much! I learned a lot. You are added to my new favorite tutors list. Have a great weekend! Bye now~

Santiago P (Tutor)
[00:29:05] OK, grea! Glad to have helped you. Have a good night. Bye.