Writing Equations based on a table - Nicole Forrester



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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