Write a rule for the following functions. i need fast!

  20.  y = 3·3^x

  21.  y = (1/3)^x

Step-by-step explanation:

These exponential functions can be written in the form ...

  y = a·b^x

where a is the value of y when x=0, and b is the common ratio between terms that have x different by 1.

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20. The ratio is 9/3 = 3; the multiplier is 3 (the value of y when x=0), so the function is ...

  y = 3·3^x

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21. The ratio is (1/3)/1 = 1/3; the multiplier is 1, so the function is ...

  y = (1/3)^x

Alternate solution

Each of these can be written in a more compact form:

  20: y = 3^(x+1)

  21: y = 3^(-x)

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.