Question

one college states that the number of men, $m$, and the number of women, $w$, receiving bachelor degrees $t$ years since 1980 can be modeled by the functions $m(t)=526 - t$ and $w(t)=474 + 2t$ respectively. let $n$ be the total number of students receiving bachelors degrees at that college $t$ years since 1980. write a formula for $n(t)$ in terms of $m(t)$ and $w(t)$. $n(t)=$ write a formula for $n(t)$ in terms of $t$. $n(t)=$

Explanation:

Step1: Understand the relationship

The total number of students $N(t)$ is the sum of the number of men $M(t)$ and the number of women $W(t)$. So $N(t)=M(t)+W(t)$.

Step2: Substitute the given functions

We know $M(t) = 526 - t$ and $W(t)=474 + 2t$. Substitute them into the above - formula: $N(t)=(526 - t)+(474 + 2t)$.

Step3: Simplify the expression

Combine like - terms: $N(t)=526+474 - t+2t=1000 + t$.

Answer:

$N(t)=M(t)+W(t)$
$N(t)=1000 + t$