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

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

Answer 2

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`