Question

Which is an exponential decay function?
A.f(x) = (7/4)x
B.f(x) = (4/5)–x
C.f(x) = (8/7)–x
D.f(x) = (9/2)x

Answer 1

hint, change first to positive exponents

Answer 2

when base of the function is between 0 and 1

Answer 3

\(\large\color{black}{ \displaystyle {\rm y}=a({\rm b})^x }\)

this function represents an exponential decay
when \(b\) satisfies the following condition: \(0>b>1\)

this function represents an exponential growth
when \(b\) satisfies the following condition: \(b>1\)

~ when \(b=1\) it is just a line \(y=a{\rm b}\) (ab is a constant)
~ when \(b=0\) it is just a line \(y=a\) (a is a constant)

this is not an exponential function
(wouldn't even call it a function, or at least not explicit)
when \(b<0\).

Answer 4

(\(a\), however, can have any value as long as \(a\) is a real number)