question 1 of 17 < > (a) if n = 4, what is δt? what are t0,t1,t2,t3,t4? what are f(t0),f(t1),f(t2),f(t3),f(t4…

Explanation:

Step1: Calculate $\Delta t$

The time - interval $\Delta t$ is calculated by the formula $\Delta t=\frac{b - a}{n}$, where $a = 0$, $b = 16$ and $n = 4$. So $\Delta t=\frac{16-0}{4}=4$.

Step2: Determine $t_i$ values

The values of $t_i$ are given by $t_i=a + i\Delta t$. For $i = 0$, $t_0=0+0\times4 = 0$; for $i = 1$, $t_1=0 + 1\times4=4$; for $i = 2$, $t_2=0+2\times4 = 8$; for $i = 3$, $t_3=0+3\times4 = 12$; for $i = 4$, $t_4=0+4\times4 = 16$.

Step3: Determine $f(t_i)$ values

We read the values of $f(t)$ from the table. When $t_0 = 0$, $f(t_0)=28$; when $t_1 = 4$, $f(t_1)=26$; when $t_2 = 8$, $f(t_2)=25$; when $t_3 = 12$, $f(t_3)=24$; when $t_4 = 16$, $f(t_4)=22$.

Answer:

$\Delta t = 4$ $t_0 = 0$, $f(t_0)=28$ $t_1 = 4$, $f(t_1)=26$ $t_2 = 8$, $f(t_2)=25$ $t_3 = 12$, $f(t_3)=24$ $t_4 = 16$, $f(t_4)=22$