Answer:
The equation representing how old Monique son is [tex]\mathbf{a = 2 + \dfrac{8}{21}(q-34)}[/tex]
Step-by-step explanation:
From the given information:
A linear function can be used to represent the constant growth rate of Monique Son.
i.e.
[tex]q(t) = \hat q \times t + q_o[/tex]
where;
[tex]q_o[/tex] = initial height of Monique's son
[tex]\hat q[/tex] = growth rate (in)
t = time
So, the average boy grows approximately 2 5/8 inches in a year.
i.e.
[tex]\hat q = 2 \dfrac{5}{8} \ in/yr[/tex]
[tex]\hat q = \dfrac{21}{8} \ in/yr[/tex]
Then; from the equation [tex]q(t) = \hat q \times t + q_o[/tex]
[tex]34 = \dfrac{21}{8} \times 0 + q_o[/tex]
[tex]q_o = 34\ inches[/tex]
The height of the son as a function of the age can now be expressed as:
[tex]q(t) = \dfrac{21}{8} \times t + 34[/tex]
Then:
Making t the subject;
[tex]q - 34 = \dfrac{21}{8} \times t[/tex]
[tex]t = \dfrac{8}{21}(q-34)[/tex]
and the age of the son i.e. ( a (in years)) is:
a = 2 + t
So;
[tex]\mathbf{a = 2 + \dfrac{8}{21}(q-34)}[/tex]
SO;
if q (growth rate) = 50 inches tall
Then;
[tex]\mathbf{a = 2 + \dfrac{8}{21}(50-34)}[/tex]
[tex]\mathbf{a = 2 + \dfrac{8}{21}(16)}[/tex]
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.
