Question 2

We will find the number of members remaining after certain hours.

Step 1 — Calculate members after 1, 2, and 3 hours

The rally starts with 120 members. Each hour, 9 members drop out. Let's find the members after 1 hour.

$120 - 9 \times 1$

$= 120 - 9$

$\boxed{111 \text{ members}}$

Now, let's find the members after 2 hours.

$120 - 9 \times 2$

$= 120 - 18$

$\boxed{102 \text{ members}}$

Finally, let's find the members after 3 hours.

$120 - 9 \times 3$

$= 120 - 27$

$\boxed{93 \text{ members}}$

Step 2 — Find a linear expression for $n$ hours

We observe a pattern from the previous step. After 1 hour, members are $120 - (9 \times 1)$. After 2 hours, members are $120 - (9 \times 2)$. After 3 hours, members are $120 - (9 \times 3)$. Let $M_n$ be the number of members after $n$ hours. The number of members leaving is $9$ times the number of hours.

$M_n = 120 - 9 \times n$

$\boxed{M_n = 120 - 9n}$

Answer

(i) After 1 hour, 111 members remain. (ii) After 2 hours, 102 members remain. (iii) After 3 hours, 93 members remain. (iv) The linear expression is $M_n = 120 - 9n$.