Math Snap

STEP 1

Assumptions1. The altitude $a$ (in feet) of a plane $t$ minutes after takeoff is given by $a=3400 t+600$.
. We need to find the time $t$ when the altitude $a$ is21,000 feet.

STEP 2

First, we need to set up the equation to solve for $t$. We know that the altitude is21,000 feet, so we can set $a$ equal to21,000 and solve for $t$.
$$3400 t +600 =21000$$

STEP 3

Subtract600 from both sides of the equation to isolate the term with $t$.
$$3400 t =21000 -600$$

STEP 4

Calculate the right side of the equation.
$$3400 t =20400$$

STEP 5

Now, divide both sides of the equation by3400 to solve for $t$.
$$t = \frac{20400}{3400}$$

Calculate the value of $t$.
$$t = \frac{20400}{3400} =6$$The plane is at an altitude of21,000 feet6 minutes after takeoff.