Writing Equations based on a table
Writing Exponential Functions Name______________________________
|1.) Go to “table” in your calculator and make|3.) Here are some linear functions. |Write an explicit equation for the table. (Hint! |
|a table for the following equations. What do|Which are equivalent? |First determine which type of function it is.) |
|you notice? |A.) [pic] | |
| |B.) [pic] |Remember, |
|A.) [pic] |C.) [pic] |y – y1 = m(x – x1) for lines |
|x |D.) [pic] |f(x) = #(base)exponent for exponential |
|y | | |
| | |7.) |
|0 |4.) Here are some exponential functions. |x |
| |Which are equivalent? |y |
| |A.) [pic] | |
|1 |B.) [pic] |1 |
| |C.) [pic] |12 |
| |D.) [pic] | |
|2 | |2 |
| | |14 |
| | | |
|3 |5.) Write linear, quadratic, or exponential for each: |3 |
| | |16 |
| |x | |
| |y |4 |
|B.) [pic] | |18 |
|x |0 | |
|y |0 | |
| | | |
|0 |1 |8.) |
| |1 |x |
| | |y |
|1 |2 | |
| |4 |1 |
| | |60 |
|2 |3 | |
| |9 |2 |
| | |50 |
|3 | | |
| |x |3 |
| |y |40 |
| | | |
|C.) [pic] |0 |4 |
|x |0 |30 |
|y | | |
| |1 | |
|0 |2 | |
| | | |
| |2 |9.) |
|1 |4 |x |
| | |y |
| |3 | |
|2 |6 |1 |
| | |3 |
| | | |
|3 |x |2 |
| |y |9 |
| | | |
| |0 |3 |
|2.) Write f(x) in three other ways given that |1 |27 |
|[pic] | | |
| |1 |4 |
|x |2 |81 |
|y | | |
| |2 | |
|0 |4 | |
| | | |
| |3 |10.) |
|1 |8 |x |
| | |y |
| | | |
|2 | |1 |
| | |200 |
| | | |
|3 | |2 |
| |6.) Write linear, quadratic, or exponential for each: |100 |
| |A.) The y-values have a constant rate of change | |
| |B.) The rate of change of the rate of change is constant. |3 |
|[pic] _________________ |C.) The y-values have a ratio |50 |
| | | |
|[pic] _________________ | |4 |
| | |25 |
|[pic] _________________ | | |
| | | |
| | | |
| | | |
| | |11.) |
| | |x |
| | |y |
| | | |
| | |1 |
| | |5 |
| | | |
| | |2 |
| | |25 |
| | | |
| | |3 |
| | |125 |
| | | |
| | |4 |
| | |625 |
| | | |
|Write an explicit equation for the table or situation.|21.) Jessica started with 1 friend, and each year she|25.) Jenna started with 3 friends, and each year her |
|(Hint! First determine which type of function it is.)|gained two more friends |number of friends tripled. |
| |x |x |
| |y |y |
|15.) | | |
|x |0 |0 |
|y | | |
| | | |
|1 |1 |1 |
|4 | | |
| | | |
|2 |2 |2 |
|16 | | |
| | | |
|3 |3 |3 |
|64 | | |
| | | |
|4 | | |
|256 | |26.) Jason had 3 friends by the end of the first |
| |22.) Jennifer started with 1 friend, and each year |year, and each year his number of friends tripled. |
| |her number of friends doubled. |x |
|16.) |x |y |
|x |y | |
|y | |1 |
| |0 | |
|1 | | |
|5 | |2 |
| |1 | |
|2 | | |
|1 | |3 |
| |2 | |
|3 | | |
|[pic] | |4 |
| |3 | |
|4 | | |
|[pic] | | |
| | | |
| | |27.) Make up your own linear function and write the |
|17.) |23.) Mike started with 3 friends, and each year his |equation for it. |
|x |number of friends doubled. | |
|y |x |x |
| |y |y |
|1 | | |
|18 |0 | |
| | | |
|2 | | |
|6 |1 | |
| | | |
|3 | | |
|2 |2 | |
| | | |
|4 | | |
|[pic] |3 | |
| | | |
| | | |
|18.) | | |
|x | |Eqn: _____________ |
|y | | |
| |24.) Jason had with 5 friends by the end of the first| |
|1 |year, and each year his number of friends doubled. |28.) Make up your own exponential function and write |
|-4 |x |the equation for it. |
| |y | |
|3 | |x |
|-2 |1 |y |
| | | |
|5 | | |
|0 |2 | |
| | | |
|7 | | |
|2 |3 | |
| | | |
| | | |
|19.) |4 | |
|x | | |
|y | | |
| | | |
|1 | | |
|2 | | |
| | |Eqn: _____________ |
|2 | | |
|1 | | |
| | | |
|3 | | |
|[pic] | | |
| | | |
|4 | | |
|[pic] | | |
| | | |
| | | |
|20.) | | |
|x | | |
|y | | |
| | | |
|0 | | |
|4 | | |
| | | |
|1 | | |
|8 | | |
| | | |
|2 | | |
|16 | | |
| | | |
|3 | | |
|32 | | |
| | | |
| | | |
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