Exponential equations
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The document discusses how to write exponential equations from tables of x and y values. It explains that the equations take the form y=ab^x, where a is the initial y value when x is 0, and b is found by dividing subsequent y values. Two examples are worked through, finding the a and b values and writing the full equations.
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Exponential equations
- 1. Writing exponential equations Given a table, you will look at the initial amount and look for a pattern in the y-column and determine the equation.
- 2. Basic equation The equations will be in the form: y=ab^x You fill in 'a' with the initial value. Look where x is zero. You find 'b' by dividing your y-values.
- 3. Write the equation x y -1 5 0 10 1 20 2 40 3 80
- 4. Answer Find 'a' from where x=0. That is 10. Find 'b' by dividing your y-values. 10/5=2 20/10=2 40/20=2 So, b=2
- 5. So, write the equation y=10(2)^x
- 6. Try one more x y -2 64 -1 16 0 4 1 1
- 7. Answer Find 'a' from where x=0. That is 4. Find 'b' by dividing your y-values. 16/64=1/4 4/16=1/4 1/4=1/4 So, b=1/4
- 8. Write the equation Y=4(1/4)^x