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
