What conclusions can be made about the amount of money in each account if f represents Molly's account and g represents her brother's account?

(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

Next, we test each option

(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

b

2

−

b

b

3

+

7

b

2

+

14

b

+

6

%

−

3

b

3

+

7

b

2

+

14

b

+

6

%

step-by-step explanation:

practice. practice. practice.