Question

Which is an exponential decay function? f(x) = 3over4(7over4)^x f(x) =2over3(4over5)^–x f(x) = 3over2(8over7)^–x f(x) = 1over3(9over2)^x

Answer 1

In exponential decay, the value under the exponent must be less than 1 and more than 0
but wait, we have exponents that are negative values, that's interesting
it's a trick, we need to convert it to form $f(x)=ab^x$
remember that $(\frac{a}{b})^{-1}=\frac{b}{a}$
also that $a^{bc}=(a^b)^c$
therefor $f(x)=a(\frac{b}{c})^{-x}=a((\frac{b}{c})^{-1})^x=a(\frac{c}{b})$
so those ones that have the -x exponent, we need to flip the fraction

first one is 7/4, that is more than1

2nd one has a negative exponent so it becomes (3/4)(5/4)^x and 5/4 is greater than 1

3rd one has negative exponent so it becomes (3/2)(7/8)^x and 7/8 is less than 1

4th one is 9/2 and that's more than 1


3rd one is answer or $f(x)=(\frac{3}{2})(\frac{8}{7})^{-x}$ is an exponential decay function