When you are trying to determine if a function is growing or decaying, is important to convert the decimals within the function to check how fast the denominator and numerator are growing. If the denominator is growing faster (is bigger) than the denominator, the function is decaying, and if the numerator is growing faster (bigger) than the denominator, the function is growing.
[tex]3.5 = \frac{7}{2} [/tex] therefore [tex]y=( \frac{7}{2})^ \frac{t}{12} [/tex]
Since the variable t is in the numerator of the fractional exponent and the the numerator (7) is bigger than the denominator (2), the function is growing.
[tex]f(x)= \frac{1}{4} (2^{t}) [/tex] this one is easy, the number raised to the variable t is an integer, so the function is growing.
[tex]0.99= \frac{99}{100}[/tex] therefore [tex]y=10( \frac{99}{100} )^{t} [/tex] Since the denominator (100) is bigger than the numerator (99), the function is decaying.
We can conclude that he first tow function are growing and the last one is decaying.
