Answer:
(b) is true
Step-by-step explanation:
Given
Molly
--- starting balance
--- monthly rate
Her brother
---- starting balance
--- annual rate
Required
Determine which option is true
First, we calculate her brother's function.
The function is an exponential function calculated as:

Where 
So, we have:




Hence:

Next, we calculate Molly's function (a linear function)
The monthly function is:

So, we have:

Annually, the function will be:


So, we have:

At this point, we have:
---- Molly
---- Her brother
<u>Next, we test each option</u>
(a): Molly's account will have a faster rate of change over [32,40]
We calculated Molly's function to be:

The slope of a linear function with the form:
is m
By comparison:

Since Molly's account is a linear function, the rate of change over any interval will always be the same; i.e.

For his brother:
Rate of change is calculated using:



Calculate g(40) and g(32)



So, we have:



By comparison: 
Hence, her brother's account has a faster rate over [32,40]
(a) is false
(b): Molly's account will have a slower rate of change over [24,30]
--- Molly's rate of change
For his brother:



Calculate g(30) and g(24)



So, we have:




By comparison: 
Hence, Molly's account has a slower rate over [24,30]
(b) is false
(c): Molly's account will have a slower rate of change over [0,4]
--- Molly's rate of change
For his brother:



Calculate g(4) and g(0)



So, we have:




By comparison: 
Hence, Molly's account has a faster rate over [0,4]
(c) is false