Question

During a recent period of time, the numbers (in thousands) of males M and females F who attend degree-granting institutions in the United States can be modeled by

M=0.752-79.5t +9020
F= 22.441²264.1t+11,971
where t is time in years. Write a polynomial in standard form to
model the total number of people attending degree-granting institutions. Then interpreted its constant term.

Answer 1

The constant term (21,991) in the polynomial P(t) = 22.441t^2 + 184.6t + 21,991 signifies the initial total attendance at degree-granting institutions when time (t) is zero.

To find the polynomial in standard form that models the total number of people attending degree-granting institutions, you add the expressions for M and F:

P(t) = M + F

Given that:

M = 0.752t - 79.5t + 9020

F = 22.441t^2 + 264.1t + 11,971

Now, substitute these into the total attendance expression:

P(t) = (0.752t - 79.5t + 9020) + (22.441t^2 + 264.1t + 11,971)

Combine like terms and write the polynomial in standard form:

P(t) = 22.441t^2 + (264.1 - 79.5)t + (9020 + 11,971)

P(t) = 22.441t^2 + 184.6t + 21,991

So, the polynomial in standard form that models the total number of people attending degree-granting institutions is:

P(t) = 22.441t^2 + 184.6t + 21,991

Now, let's interpret the constant term (the term without a variable, 21,991):

The constant term represents the initial or baseline attendance when t = 0. In this context, it would mean the initial total number of people attending degree-granting institutions. Therefore, when t = 0, the constant term (21,991) represents the estimated total attendance at the starting point of the time period in question.