3.3+Making+a+Difference


 * __Problem 3.3: Making a Difference__**

Investigation 3 Essential Question How can I show a pattern of repeated division? 10 || $1775 $1846 ||
 * Big Idea** The rate at which many things grow or decay can often be described mathematically.
 * Sam’s Donation **
 * Sam gave some of his coins to his sister to her pay college expenses. The value of the reaming collection was $1250. **
 * A.** **Suppose the Value of the reaming coins increased by 4% each year. Make a table shoing the value of the collection each year for the next 10 years.**
 * Sam's Donation**
 * Years ( 4% Increase Each Year || Collection (Coins) ||
 * 0 || $1250 ||
 * 1 || $1300 ||
 * 2 || $1352 ||
 * 3 || $1406 ||
 * 4 || $1462 ||
 * 5 || $1520 ||
 * 6 || $1580 ||
 * 7 || $1642 ||
 * 8 || $1707 ||
 * 9


 * Maya’s Donation**
 * Years (4% Increase Each Year || Collection (Baseball Cards) ||
 * 0 || $2500 ||
 * 1 || $2600 ||
 * 2 || $2704 ||
 * 3 || $2812 ||
 * 4 || $2924 ||
 * 5 || $3040 ||
 * 6 || $3161 ||
 * 7 || $3287 ||
 * 8 || $3418 ||
 * 9 || $3554 ||
 * 10 || $3696 ||

A. Graph is shown above B. **Compare the values of the collections over the 10 year period. How does the initial value of the collection affect the yearly increase in value?** The initial value is the starting point or the intercept. Since the starting or initial value is larger for Maya’s than Sam’s, it will be pretty obvious that the larger starter number will likely to collect more.

C. **How does the initial value of each collection affect the growth factor?** The growth factor here will be 1 for both collections. The method is basically finding the ratio between the **Value in Year //n/// Value in Year //n – 1.//** To find the growth factor you have use the method of having the growth factor being added to decimal which was converted from the given percentage and then you will get the value. Plug in the value of n to the formula the book has already given you to find the ratio between values. //__V= $1250 x 1t__// 1250 x 30 = $37,500 after 30 years of collecting.
 * D. Write an Equation for the Value, V of Sam’s $1250 coin collection after t years.**
 * E. Solve your equation to find the value of Sam’s collection after 30 years.**


 * __Problem 3.3 Follow Up__**

Value = $2400 x 1.05 x 1.05 x 1.05 x 1.05 He is assuming that the initial value is $2400 and the rate of increasing in value is 1.05 or the growth factor In this case and the number of years is 4 years because the you are multiply 1.05 four times. $2400 will initially start at 0.
 * 1.** **Sam made the following calculation to predict the value of his aunt’s stamp collection several years from now.**
 * 1a. What Initial value, rate of increase in value, and number or years is Sam assuming?**

The Collection would be worth $3036.08. Because you just multiply 1.05 which is technically one more year to the equation shown and given above. I found out the growth factor by using $2400 as my initial value.
 * 1b**. **The result of Sam’s calculation is $2917.22. If the value continued to increase at this rate, how much would the collection be worth in one more year?**
 * 2.** **Find the growth factor associated with each percent increase.**
 * a.** 30% = 1.00032 **b.** 15% = 1.00036 **c.** 5% = 1.00039 **d.** 75 % = 1.00023