Exponential Functions - An exponential pattern is something

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Exponential Functions - An exponential pattern is something Powered By Docstoc
					                                           Exponential Functions

An exponential pattern is something that grows or decays by a multiple of some number. For
example, something that doubles, multiplies by 2 every time, and something that triples,
multiplies by 3 every time.

The general exponential equation is y = a(b)x, where a is the starting point (the number at
zero) and b is the number you are multiplying by. If b is bigger than 1, the equation is
growth, and if b is less than 1, the equation is decay.

Ex:      x        y                                      x         y
                                                                              The starting point
        0         2          The starting point          0     16
         1        6                                      1     8
                        Multiplying by 3                                 Dividing by 2…so, multiplying by ½
        2         18                                     2         4
        3         54                                     3         2

      This one’s growth                               This one’s decay
      y = 2(3)x                                       y = 16(½)x


When dealing with percentage growth or decay, like interest problems or population
problems, the general formulas are:

       Growth:         A = P(1 + r)t                   A = Final amount
                                                       P = Initial amount
       Decay:          A = P(1 – r)t                   r = rate (in decimal form)
                                                       t = time in years

Ex:
1.     In 1800, Sallie Mae just found out that one of her ancestors invested $300 in a
       savings account that paid 4% interest annually. Find the account balance after the
       year 1950.

       P = $300                        Equation A = 300 (1 + 0.04)150

       r = 0.04                        using a calculator, typing in 300(1+0.04)150

       t = 150                         the account balance is $107676.80


2.     Suppose the acreage of forest is decreasing by 4% every year because of
       development. If there are currently 6,000,000 acres of forest, determine the
       amount of forest left after 15 years.

       P = 6000000                     Equation A = 6000000(1 – 0.04)15

       r = 0.04                        using a calculator, typing in 6000000(1 – 0.04)15

       t = 15                          the forest acreage is 3,252,518.28 acres
Practice Problems

1.   y = 8(1.04)x

        a) What is the initial amount?

        b) What is the growth factor?

2.   y = 7(0.43)x

        a) What is the initial amount?

        b) What is the decay factor?

3.
             x              y
             1              1                 a) What is the initial amount?
             2              4
                                              b) What is the growth factor?
             3             16
             4            64                  c) What is the equation?
             5            256

4.
             x              y
             1             81                 a) What is the initial amount?
             2             27                 b) What is the decay factor?
             3              9
             4              3                 c) What is the equation?
             5              1


Use the following tables to answer the questions #5 - 6.

A)      x           y           B)     x          y      C)     x        y     D)   x   y
         1           1                 1         2              1        1          1   1
        2           0.5                2         8              2        11         2   4
        3        0.25                  3         18             3        21         3   16
        4        0.125                 4         32             4        31         4   64



5. Which table represents an exponential growth function?

6. Which table represents an exponential decay function?



7. Write an equation that represents the data in the table.

 x       1     2           3      4      5
 y      75    30          12     4.8   1.92
8. Write an equation that represents the data in the table.

 x         0        1      2       3     4
 y       3.125    6.25    12.5    25     50



9.        For California, the population in 1900 was 1.77 million. Since then, the population has
          grown at a rate of 3% per year. According to this rate, what was the population in
          2000?


10.       A $55,000 purchase depreciates at 16% each year. What would the value be after 10
          years?




Answers

1. a) 8 b) 1.04

2. a) 7 b) 0.43

3. a) ¼ (remember it’s where x= 0)

      b) 4

      c) y = ¼ (4)x

4. a) 243

      b) 1/3

      c) y = 243 (1/3)x

5. D
6. A
7. y = 187.5(.4)x

8. y = 3.125(2)x

9. The population in 2000 was 34016978.61 people
10. The value is $9619.57

				
Lingjuan Ma Lingjuan Ma MS
About work for China Compulsory Certification. Some of the documents come from Internet, if you hold the copyright please contact me by huangcaijin@sohu.com