Question

6-60. figure 3 of a tile pattern has 11 tiles, while figure 4 has 13 tiles. the pattern grows at a constant rate. homework help

a. write an equation to represent this situation.

b. which figure will contain 1015 tiles?

Explanation:

Step1: Identify linear relationship parameters

We have two points: $(n_1, t_1)=(3,11)$ and $(n_2, t_2)=(4,13)$. The slope (rate of change) $m$ is calculated as:
$m = \frac{t_2 - t_1}{n_2 - n_1} = \frac{13-11}{4-3}=2$

Step2: Find y-intercept (initial value)

Use the linear form $t=mn+b$, substitute $n=3$, $t=11$, $m=2$:
$11 = 2(3) + b$
$11=6+b$
$b=11-6=5$

Step3: Write the linear equation

Substitute $m=2$ and $b=5$ into $t=mn+b$:
$t=2n+5$

Step4: Solve for n when t=1015

Substitute $t=1015$ into $t=2n+5$:
$1015=2n+5$
$2n=1015-5=1010$
$n=\frac{1010}{2}=505$

Answer:

a. $t=2n+5$ where $t$ is the number of tiles and $n$ is the figure number
b. Figure 505