91Ó°ÊÓ

We are given that,

The road has a positive grade, $g$

And we begin driving at an altitude of$a_0$

We need to indicate altitude after driving distance $d$on the road.

Grade $g$represents a fraction of the height of each unit. When we drive a distance of $d$, the height thus rises by $gd$.

However, the first height is $a_0$so the total height after the rise is $a_0+gd$.

Hence the equation is, $a=a_0+gd$

Here, $a$is the altitude after covering some distance

We need to find out the $y$-intercept and slope of the equation.

From part (a)

The $y$-intercept is the constant in the equation i.e. $a_0$

And the slope is the coefficient of$d$, i.e.,$g$

We need to find the value of altitude i.e.$a$

As the values are,

$$\begin{gathered} a_0=1 \\ g=5\%=0.05 \end{gathered}$$

So, from part (a) and above values we get,

$a=a_0+gd=1+0.05d$

We need to find the value $a$at a distance $d=10miles$and other conditions same as that of part (c)

From part (c) we get

$a=1+0.05d=1+\left(0.05×10\right)=1+0.5=1.5$

Hence the reached altitude is,$1.5miles$

We need to find the distance drove.

From part (c)

$a=a_0+gd=1+0.05d$

As $a=3$

So,

$$\begin{gathered} 3=1+0.05d \\ 2=0.05d \\ d=40 \end{gathered}$$

Therefore, distance drove is $d=40miles$