Mathematical+Reflections,+p+44

** **  NG  ****  Big Idea: The rate at which many things grow or decay can often be described mathematically. **** Essential Question: How can I show a pattern of repeated division? **** Notes From Class: compound growth- a pattern of change in which the percent is applied to the current increased value. (3.2 Vocab) **
 * Mathematical Reflections, pg. 44[[image:NG_MR_3_fish.jpg width="218" height="164" align="right"]] **
 * 1/2/09

**a. How would you decide whether the population was growing exponentially?**
 * 1. Suppose you had data about the growth of a fish population in a lake over several years.**
 * You could graph the data points and determine whether the rate of change was exponential or linear, by, for example, seeing how quickly the data increased. You could also observe the shape the data created on the graph; if a curve appeared, then the population was growing exponentially. **

First, you would write a P, to stand for population. Then you would write the starting population; for example, 100. Next you need to find the growth factor. You can do that by using this equation: pop. in year n / pop. in year n-1. The factor might turn out to be 1.05. So, the equation would be P=100(1.05^t), where t = year. = = A growth rate of 20% is almost the same as an exponential growth of 1.2. '1.2' can also be written as '1.20'. This means to get the next year's data, you add 100% of the previous year's data and 20% of the previous year's data. That totals to 120%, or 1.2 as the exponential growth.
 * b. If the population growth appeared to be exponential, how would you use the data to write an equation for growth?**
 * 2. How is a growth rate of 20% related to an exponential growth of 1.2?**

**a. Predict what an apartment that now rents for $1500 per month will rent for 1 year from now. Explain your work.** **b. Predict what an apartment that now rents for $1500 per month will rent for each year for the next 5 years. Explain your work**   **.** YEAR 2- $2160 YEAR 3- $2592 YEAR 4- $3110.40 YEAR 5- $3732.48
 * 3. Suppose rents in a particular area are increasing by 20%** **per year****.**
 * An apartment that rents $1500 per month now will rent $1800 per month a year from now. I found this out by creating an equation, using 1500 as the starting value and turning the 20% into a growth factor of 1.2. **
 * I used my equation predict the rent for the next 5 years. **

**c. Write an equation that you could use to predict the rent for the $1500 apartment**  //**t**// **years from now.**           r = 1500(1.2^ //t//)

**In this chapter, I learned a lot more about growth factors. I discovered easier ways to convert percents into growth factors, find a growth factor from a set of data, and to incorporate these growth factors into equations. This chapter's problems showed me ways that I could apply this knowledge in real-life, which was very helpful. So, this chapter really increased my ability to work with growth factors.
 * __Summary__