Two towns are located at points A(0,20) and B(4,60). The number of customers in a shop increases by 3 each day, starting with 7 customers on the first day. Generate models for the road and customer gr

The formula for the slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Let $(x_1, y_1) = (0, 20)$ and $(x_2, y_2) = (4, 60)$.

We know the slope $m=10$.
Since one of the points is $(0,20)$, the y-intercept ($c$) is 20.
Substitute $m=10$ and $c=20$ into the equation.

The model (equation) that represents the road is $\boxed{y = 10x + 20}$.

The number of customers on the first day ($a_1$) is 7.
The customers kept on increasing by 3 daily, so the common difference ($d$) is 3.

The formula for the $n$-th term of an arithmetic progression is $a_n = a_1 + (n-1)d$.
Substitute $a_1 = 7$ and $d = 3$ into the formula.

The model (nth term) relating the number of days ($n$) and customers ($a_n$) is $\boxed{a_n = 3n + 4}$.

Substitute $n=20$ into the model $a_n = 3n + 4$.

The number of customers after 20 days will be $\boxed{64}$.