Question

which value of a in the exponential function below would cause the function to shrink? f(x) = a(3/2)^x a.4/5 b.5/4 c.3/2 d.7/4

Answer 1

we know that

We can enlarge or shrink  the function in the y-direction by multiplying the function by a constant.

we have

$y=a(b^{x})$

if $a> 1$ -------> the function enlarge

if $0< a < 1$ -------> the function shrinks

case A) $a=4/5$

$0 < (4/5)< 1$ ------> the function shrinks

case B) $a=5/4$

$(5/4)> 1$ ------> the function enlarge

case C) $a=3/2$

$(3/2)> 1$ ------> the function enlarge

case D) $a=7/4$

$(7/4)> 1$ ------> the function enlarge

therefore

the answer is

$a=4/5$

Answer 2

F(x) will shrink when a < 1. i.e a = 4/5