Question

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 age of 15. Write an equation that represents how old Monique's son will be when he is 50 inches tall.( letdown represent the amount of the year since age 2)

Answer 1

The equation representing how old Monique son is
`\mathbf{a = 2 + (8)/(21)(q-34)}`

Explanation:

From the given information:

A linear function can be used to represent the constant growth rate of Monique Son.

i.e.

`q(t) = \hat q * t + q_o`

where;

`q_o` = initial height of Monique's son

`\hat q` = growth rate (in)

t = time

So, the average boy grows approximately 2 5/8 inches in a year.

i.e.

`\hat q = 2 (5)/(8) \ in/yr`

`\hat q = (21)/(8) \ in/yr`

Then; from the equation
`q(t) = \hat q * t + q_o`

`34 = (21)/(8) * 0 + q_o`

`q_o = 34\ inches`

The height of the son as a function of the age can now be expressed as:

`q(t) = (21)/(8) * t + 34`

Then:

Making t the subject;

`q - 34 = (21)/(8) * t`

`t = (8)/(21)(q-34)`

and the age of the son i.e. ( a (in years)) is:

a = 2 + t

So;

`\mathbf{a = 2 + (8)/(21)(q-34)}`

SO;

if q (growth rate) = 50 inches tall

Then;

`\mathbf{a = 2 + (8)/(21)(50-34)}`

`\mathbf{a = 2 + (8)/(21)(16)}`

a = 2 + 6.095

a = 8.095 years

a ≅ 8 years

i.e.

Monique son will be 8 years at the time Monique is 50 inches tall.