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
`((a)/(b))^(-1)=(b)/(a)`
also that
`a^(bc)=(a^b)^c`
therefor
`f(x)=a((b)/(c))^(-x)=a(((b)/(c))^(-1))^x=a((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)=((3)/(2))((8)/(7))^(-x)` is an exponential decay function