Monique’s son just turned 2 years old and is 34 inches tall. Monique heard that the average boy will grow approximately 2 5/8 inches per year until the ago of 15. Part A: Write an equation that represents how old Monique’s son will be when he is 50 inches tall. (let X represent the amount of year since age 2)

Part B: How old will Monique’s son be when he is 50 inches tall?

a) The equation that represents how old Monique's son will be when he is 50 inches tall is .

b) Monique's son will be 8 years old when he is 50 inches tall.

Step-by-step explanation:

a) From statement we see that Monique's son grows at a constant rate and observes the following linear function:

(Eq. 1)

Where:

- Initial height of Monique's son, measured in inches.

- Growth rate, measured in inches per year.

- Time, measured in years.

The growth rate of the average boy is:

If we know that , and , then the initial height of Monique's son is:

Then, the height of Monique's son as a function of age is represented by:

(Eq. 2)

The age of Monique's son (), expressed in years, is represented by the following formula:

(Eq. 3)

Now we clear time within (Eq. 2):

Therefore, the age of Monique's son is modelled after this:

(Eq. 4)

b) If we know that , then the age of Monique's son will be:

Monique's son will be 8 years old when he is 50 inches tall.